Works by I. Németi
64 found
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| Istvan Németi [41] | I. Németi [24] |
- Modal Languages and Bounded Fragments of Predicate Logic.Hajnal Andréka,István Németi &Johan van Benthem -1998 -Journal of Philosophical Logic 27 (3):217 - 274.What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...) As a counterproposal, then, we define a large fragment of predicate logic characterized by its use of only bounded quantification. This so-called guarded fragment enjoys the above nice properties, including decidability, through an effectively bounded finite model property. (These are new results, obtained by generalizing notions and techniques from modal logic.) Moreover, its own internal finite variable hierarchy turns out to work well. Finally, we shall make another move. The above analogy works both ways. Modal operators are like quantifiers, but quantifiers are also like modal operators. This observation inspires a generalized semantics for first-order predicate logic with accessibility constraints on available assignments (cf. N´emeti 1986, 1992) which moves the earlier quantifier restrictions into the semantics. This provides a fresh look at the landscape of possible predicate logics, including candidates sharing various desirable features with basic modal logic – in particular, its decidability. (shrink)
- A Formalization of Set Theory Without Variables.István Németi -1988 - American Mathematical Soc..Completed in 1983, this work culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. Written in collaboration with Steven Givant, the book appeals to a very broad audience, and requires only a familiarity with first-order logic. It is of great interest to logicians and mathematicians interested in the foundations of mathematics, but also to philosophers interested in logic, semantics, algebraic logic, or the methodology of the deductive sciences, and to (...) computer scientists interested in developing very simple computer languages rich enough for mathematical and scientific applications. The authors show that set theory and number theory can be developed within the framework of a new, different, and simple equational formalism, closely related to the formalism of the theory of relation algebras. There are no variables, quantifiers, or sentential connectives. Predicates are constructed from two atomic binary predicates (which denote the relations of identity and set-theoretic membership) by repeated applications of four operators that are analogues of the well-known operations of relative product, conversion, Boolean addition, and complementation. All mathematical statements are expressed as equations between predicates. There are ten logical axiom schemata and just one rule of inference: the one of replacing equals by equals, familiar from high school algebra. Though such a simple formalism may appear limited in its powers of expression and proof, this book proves quite the opposite. The authors show that it provides a framework for the formalization of practically all known systems of set theory, and hence for the development of all classical mathematics. The book contains numerous applications of the main results to diverse areas of foundational research: propositional logic; semantics; first-order logics with finitely many variables; definability and axiomatizability questions in set theory, Peano arithmetic, and real number theory; representation and decision problems in the theory of relation algebras; and decision problems in equational logic. (shrink)
- A logic road from special relativity to general relativity.Hajnal Andréka,Judit X. Madarász,István Németi &Gergely Székely -2012 -Synthese 186 (3):633 - 649.We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
- Algebraization of quantifier logics, an introductory overview.István Németi -1991 -Studia Logica 50 (3):485 - 569.This paper is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics. The paper has a survey character, too. The most frequently used algebras like cylindric-, relation-, polyadic-, and quasi-polyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some (...) directions we tried to give an overview of the most recent results and research trends, too. (shrink)
- Non-Turing Computations via Malament-Hogarth space-times.Gábor Etesi &István Németi -2002 -International Journal of Theoretical Physics 41:341--70.
- Mutual definability does not imply definitional equivalence, a simple example.Hajnal Andréka,Judit X. Madarász &István Németi -2005 -Mathematical Logic Quarterly 51 (6):591-597.We give two theories, Th1 and Th2, which are explicitly definable over each other , but are not definitionally equivalent. The languages of the two theories are disjoint.
- (1 other version)On universal algebraic constructions of logics.H. Andréka,T. Gergely &I. Németi -1977 -Studia Logica 36 (1-2):9 - 47.
- Omitting types for finite variable fragments and complete representations of algebras.Hajnal Andréka,István Németi &Tarek Sayed Ahmed -2008 -Journal of Symbolic Logic 73 (1):65-89.We give a novel application of algebraic logic to first order logic. A new, flexible construction is presented for representable but not completely representable atomic relation and cylindric algebras of dimension n (for finite n > 2) with the additional property that they are one-generated and the set of all n by n atomic matrices forms a cylindric basis. We use this construction to show that the classical Henkin-Orey omitting types theorem fails for the finite variable fragments of first order (...) logic as long as the number of variables available is > 2 and we have a binary relation symbol in our language. We also prove a stronger result to the effect that there is no finite upper bound for the extra variables needed in the witness formulas. This result further emphasizes the ongoing interplay between algebraic logic and first order logic. (shrink)
- Algebraic Logic.H. Andréka,James Donald Monk &I. Németi -1991 - North Holland.This volume is not restricted to papers presented at the 1988 Colloquium, but instead aims to provide the reader with a (relatively) coherent reading on Algebraic Logic, with an emphasis on current research. To help the non-specialist reader, the book contains an introduction to cylindric and relation algebras by Roger D. Maddux and an introduction to Boolean Algebras by Bjarni Joacute;nsson.
- Testing Definitional Equivalence of Theories Via Automorphism Groups.Hajnal Andréka,Judit Madarász,István Németi &Gergely Székely -2024 -Review of Symbolic Logic 17 (4):1097-1118.Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, (...) Glymour and Halvorson. (shrink)
- On neat reducts of algebras of logic.Tarek Sayed Ahmed &Istvan Németi -2001 -Studia Logica 68 (2):229-262.SC , CA , QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras, and quasipolyadic equality algebras of dimension , respectively. Generalizing a result of Németi on cylindric algebras, we show that for K {SC, CA, QA, QEA} and ordinals , the class Nr K of -dimensional neat reducts of -dimensional K algebras, though closed under taking homomorphic images and products, is not closed under forming subalgebras (i.e. is not a variety) if (...) and only if > 1.From this it easily follows that for 1 , the operation of forming -neat reducts of algebras in K does not commute with forming subalgebras, a notion to be made precise. (shrink)
- Twin Paradox and the Logical Foundation of Relativity Theory.Judit X. Madarász,István Németi &Gergely Székely -2006 -Foundations of Physics 36 (5):681-714.We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of (...) accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. (shrink)
- Back and Forth Between Modal Logic and Classical Logic.Hajnal Andreka,Johan van Benthem &Istvan Nemeti -1995 -Logic Journal of the IGPL 3 (5):685-720.
- Axiomatizing Relativistic Dynamics without Conservation Postulates.H. Andréka,J. X. Madarász,I. Németi &G. Székely -2008 -Studia Logica 89 (2):163-186.A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous E = mc² . The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.
- Relativistic Computers and the Turing Barrier.István Németi &Gyula Dávid -2006 -Journal of Applied Mathematics and Computation 178:118--42.
- Cylindric-relativised set algebras have strong amalgamation.I. Németi -1985 -Journal of Symbolic Logic 50 (3):689-700.
- The class of neat-reducts of cylindric algebras is not a variety but is closed w.r.t. HP.István Németi -1983 -Notre Dame Journal of Formal Logic 24:399-409.
- Finite algebras of relations are representable on finite sets.H. Andreka,I. Hodkinson &I. Nemeti -1999 -Journal of Symbolic Logic 64 (1):243-267.Using a combinatorial theorem of Herwig on extending partial isomorphisms of relational structures, we give a simple proof that certain classes of algebras, including Crs, polyadic Crs, and WA, have the `finite base property' and have decidable universal theories, and that any finite algebra in each class is representable on a finite set.
- On varieties of cylindric algebras with applications to logic.I. Németi -1987 -Annals of Pure and Applied Logic 36:235-277.
- Weakly higher order cylindric algebras and finite axiomatization of the representables.I. Németi &A. Simon -2009 -Studia Logica 91 (1):53 - 62.We show that the variety of n -dimensional weakly higher order cylindric algebras, introduced in Németi [9], [8], is finitely axiomatizable when n > 2. Our result implies that in certain non-well-founded set theories the finitization problem of algebraic logic admits a positive solution; and it shows that this variety is a good candidate for being the cylindric algebra theoretic counterpart of Tarski’s quasi-projective relation algebras.
- Axiomatizing relativistic dynamics without conservation postulates.Hajnal Andréka,Judit Madarász X.,István Németi &Gergely Székely -2008 -Studia Logica 89 (2):163 - 186.A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.
- Notions of density that imply representability in algebraic logic.Hajnal Andréka,Steven Givant,Szabolcs Mikulás,István Németi &András Simon -1998 -Annals of Pure and Applied Logic 91 (2-3):93-190.Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...) to other classes of algebras of logic, for example quasi-polyadic algebras and substitution-cylindrification algebras with and without equality, relation algebras, and special Boolean monoids. The results of op. cit. mentioned above are special cases of our general theorems. We point out an error in the proof of the Henkin-Monk-Tarski representation theorem for atomic, equality-free, quasi-polyadic algebras with rectangular atoms. The error consists in the implicit assumption of a property that does not, in general, hold. We then give a correct proof of their theorem. Henkin and Tarski also introduced the notion of a rich cylindric algebra and proved in op. cit. that every rich cylindric algebra of finite dimension satisfying certain special identities is representable. We introduce a modification of the notion of a rich algebra that, in our opinion, renders it more natural. In particular, under this modification richness becomes a density notion. Moreover, our notion of richness applies not only to algebras with equality, such as cylindric algebras, but also to algebras without equality. We show that a finite dimensional algebra is rich iff it is rectangularly dense and quasi-atomic; moreover, each of these conditions is also equivalent to a very natural condition of point density . As a consequence, every finite dimensional rich algebra of logic is representable. We do not have to assume the validity of any special identities to establish this representability. Not only does this give an improvement of the Henkin-Tarski representation theorem for rich cylindric algebras, it solves positively an open problem in op. cit. concerning the representability of finite dimensional rich quasi-polyadic algebras without equality. (shrink)
- Relation algebras from cylindric and polyadic algebras.I. Nemeti &A. Simon -1997 -Logic Journal of the IGPL 5 (4):575-588.This paper is a survey of recent results concerning connections between relation algebras , cylindric algebras and polyadic equality algebras . We describe exactly which subsets of the standard axioms for RA are needed for axiomatizing RA over the RA-reducts of CA3's, and we do the same for the class SA of semi-associative relation algebras. We also characterize the class of RA-reducts of PEA3's. We investigate the interconnections between the RA-axioms within CA3 in more detail, and show that only four (...) implications hold between them . In the other direction, we introduce a natural CA-theoretic equation MGR+, generalization of the well-known Merrry-Go-Round equation MGR of CA-theory. We show that MGR+ is equivalent to the RA-reduct being an SA, and that MGR+ implies that the RA-reduct determines the algebra itself, while MGR is not sufficient for either of these to hold. Then we investigate how different CA's a single RRA can 'generate' in the general case. We solve the first part of Problem 11 from the 'Problem Session Paper' of [2].While proving some of the statements, for others we give only outline of proof. The paper contains several open problems. A full version of this paper is under preparation.Keywords: relation algebras, cylindric algebras, polyadic algebras, algebraic logic, arrow logic, proof theory, finite variable fragments, provability with 3 variables, non-finitizability, twisting, non-standard models, neat reducts, representability. (shrink)
- Strong representability of fork algebras, a set theoretic foundation.I. Nemeti -1997 -Logic Journal of the IGPL 5 (1):3-23.This paper is about pairing relation algebras as well as fork algebras and related subjects. In the 1991-92 fork algebra papers it was conjectured that fork algebras admit a strong representation theorem . Then, this conjecture was disproved in the following sense: a strong representation theorem for all abstract fork algebras was proved to be impossible in most set theories including the usual one as well as most non-well-founded set theories. Here we show that the above quoted conjecture can still (...) be made true by choosing an appropriate set theory as our foundation of mathematics. Namely, we show that there are non-well-founded set theories in which every abstract fork algebra is representable in the strong sense, i.e. it is isomorphic to a set relation algebra having a fork operation which is obtained with the help of the real pairing function. Further, these non-well-founded set theories are consistent if usual set theory is consistent. Finally, we will discuss related developments in propositional multi-modal logics of quantification and substitution, in algebraic logic e.g. cylindric algebras, the so called finitization problem, and applications to a logic introduced and studied in Tarski-Givant [42]. In particular, representable, weakly higher order cylindric algebras are finitely axiomatizable in a set theory which admits the axiom of foundation for finite sets. (shrink)
- Shortened version appeared as.I. Németi -1991 -Studia Logica 50 (3-4):458-569.
- On A New Semantics for First-Order Predicate Logic.István Németi,Johan van Benthem &Hajnal Andréka -2017 -Journal of Philosophical Logic 46 (3):259-267.
- Cylindric Set Algebras.L. Henkin,J. D. Monk,A. Tarski,H. Andréka &I. Németi -1986 -Studia Logica 45 (2):223-225.
- General algebraic logic: A perspective on “what is logic”.Istvan Nemeti &Hajnal Andreka -1994 - In Dov M. Gabbay,What is a logical system? New York: Oxford University Press.
- Nonrepresentable relation algebras from groups.Hajnal Andréka,István Németi &Steven Givant -2020 -Review of Symbolic Logic 13 (4):861-881.A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We present our main construction in terms of polygroupoids.
- Logic Families.Hajnal Andréka,Zalán Gyenis,István Németi &Ildikó Sain -forthcoming -Studia Logica:1-47.A logic family is a bunch of logics that belong together in some way. First-order logic is one of the examples. Logics organized into a structure occur in abstract model theory, institution theory and in algebraic logic. Logic families play a role in adopting methods for investigating sentential logics to first-order like logics. We thoroughly discuss the notion of logic families as defined in the recent Universal Algebraic Logic book.
- Expressibility of properties of relations.Hajnal Andréka,Ivo Düntsch &István Németi -1995 -Journal of Symbolic Logic 60 (3):970-991.We investigate in an algebraic setting the question of which logical languages can express the properties integral, permutational, and rigid for algebras of relations.
- Nonrepresentable relation algebras from groups - addendum.Hajnal Andréka,István Németi &Steven Givant -2019 -Review of Symbolic Logic 12 (4):892-892.
- Decidable and undecidable logics with a binary modality.ágnes Kurucz,István Németi,Ildikó Sain &András Simon -1995 -Journal of Logic, Language and Information 4 (3):191-206.We give an overview of decidability results for modal logics having a binary modality. We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.
- Undecidable Varieties of Semilattice—ordered Semigroups, of Boolean Algebras with Operators, and logics extending Lambek Calculus.A. Kurucz,I. Nemeti,I. Sain &A. Simon -1993 -Logic Journal of the IGPL 1 (1):91-98.We prove that the equational theory of a semigroups becomes undecidable if we add a semilattice structure with a ‘touch of symmetric difference’. As a corollary we obtain that the variety of all Boolean algebras with an associative binary operator has a ‘hereditarily’ undecidable equational theory. Our results have implications in logic, e.g. they imply undecidability of modal logics extending the Lambek Calculus and undecidability of Arrow Logics with an associative arrow modality.
- A twist in the geometry of rotating Black holes: Seeking the cause of acausality.Christian Wüthrich,Hajnal Andréka &István Németi -manuscriptWe investigate Kerr–Newman black holes in which a rotating charged ring-shaped singularity induces a region which contains closed timelike curves (CTCs). Contrary to popular belief, it turns out that the time orientation of the CTC is oppo- site to the direction in which the singularity or the ergosphere rotates. In this sense, CTCs “counter-rotate” against the rotating black hole. We have similar results for all spacetimes sufficiently familiar to us in which rotation induces CTCs. This motivates our conjecture that perhaps (...) this counter-rotation is not an accidental oddity particular to Kerr–Newman spacetimes, but instead there may be a general and intuitively comprehensible reason for this. (shrink)
- On A New Semantics for First-Order Predicate Logic.István Németi,Johan Benthem &Hajnal Andréka -2017 -Journal of Philosophical Logic 46 (3):259-267.
- A system of logic for partial functions under existence-dependent Kleene equality.H. Andréka,W. Craig &I. Németi -1988 -Journal of Symbolic Logic 53 (3):834-839.Ordinary equational logic is a connective-free fragment of first-order logic which is concerned with total functions under the relation of ordinary equality. In [AN] (see also [AN1]) and in [Cr] it has been extended in two equivalent ways into a near-equational system of logic for partial functions. The extension given in [Cr] deals with partial functions under two relationships: a relationship of existence-dependent existence and one of existence-dependent Kleene equality. For the language that involves both relationships a set of rules (...) was given that is complete. Those rules in the set that involve only existence-dependent existence turned out to be complete for the sublanguage that involves this relationship only. In the present paper we give a set of rules that is complete for the other sublanguage, namely the language of partial functions under existence-dependent Kleene equality.This language lacks a certain, often needed, power of expressing existence and fails, in particular, to be an extension of the language that underlies ordinary equational logic. That it possesses a fairly simple complete set of rules is therefore perhaps more of theoretical than of practical interest. The present paper is thus intended to serve as a supplement to [Cr] and, less directly, to [AN]. The subject is further rounded out, and some contrast is provided, by [Rob]. The systems of logic treated there are based on the weaker language in which partial functions are considered under the more basic relation of Kleene equality. (shrink)
- On the number of generators of cylindric algebras.H. Andréka &I. Németi -1985 -Journal of Symbolic Logic 50 (4):865-873.
- The lattice of varieties of representable relation algebras.Hajnal Andréka,Steven Givant &István Németi -1994 -Journal of Symbolic Logic 59 (2):631-661.We shall show that certain natural and interesting intervals in the lattice of varieties of representable relation algebras embed the lattice of all subsets of the natural numbers, and therefore must have a very complicated lattice-theoretic structure.
- On generalizing the logic-approach to space-time towards general relativity: first steps.Judit X. Madarász,István Németi &Csaba Toke -2004 - In Vincent F. Hendricks,First-order logic revisited. Berlin: Logos. pp. 225--268.
- Algebraic logic conference, Budapest, 1988.H. Andréka,M. Ferenczi,I. Németi &Gy Serény -1989 -Journal of Symbolic Logic 54 (2):686-686.
- Connections between axioms of set theory and basic theorems of universal algebra.H. Andréka,Á Kurucz &I. Németi -1994 -Journal of Symbolic Logic 59 (3):912-923.One of the basic theorems in universal algebra is Birkhoff's variety theorem: the smallest equationally axiomatizable class containing a class K of algebras coincides with the class obtained by taking homomorphic images of subalgebras of direct products of elements of K. G. Gratzer asked whether the variety theorem is equivalent to the Axiom of Choice. In 1980, two of the present authors proved that Birkhoff's theorem can already be derived in ZF. Surprisingly, the Axiom of Foundation plays a crucial role (...) here: we show that Birkhoff's theorem cannot be derived in ZF + AC {Foundation}. even if we add Foundation for Finite Sets. We also prove that the variety theorem is equivalent to a purely set-theoretical statement, the Collection Principle. This principle is independent of $ZF \{\operatorname{Foundation}$ . The second part of the paper deals with further connections between axioms of ZF-set theory and theorems of universal algebra. (shrink)
- Complexity in the interdefinability of timelike, lightlike and spacelike relatedness of Minkowski spacetime.Hajnal Andréka,Judit X. Madarász,István Németi &Gergely Székely -2022 -Annals of Pure and Applied Logic 173 (5):103100.
- Completeness of Floyd logic.Hajnal Andreka &Istvan Nemeti -1978 -Bulletin of the Section of Logic 7 (3):115-119.This is an abstract of our paper \A characterisation of Floyd-provable programs" submitted to Theoretical Computer Science. ! denotes the set of natural numbers. Y =d fyi : i 2 !g is the set of variable symbols. L denotes the set of classical rst order formulas of type t possibly with free variables , where t is the similarity type of arithmetic, i.e. it consists of \+; ; 0; 1" with arities \2; 2; 0; 0".Export citation
Bookmark - Decision Problems for Equational Theories of Relation Algebras.H. Andréka,Steven R. Givant &I. Németi -1997 - American Mathematical Soc.."We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural numbers has a (...) decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract. (shrink)
- Modal Logics and Bounded First-Order Fragments'.H. Andréka,J. van Benthem &I. Németi -forthcoming -Journal of Philosophical Logic.
- Not all representable cylindric algebras are neat reducts.Hajnal Andréka &István Németi -1979 -Bulletin of the Section of Logic 8 (3):145-147.
- On neat reducts of algebras of logic', presented in Logic Colloquium 1996, abstract appeared in the.H. Andréka,I. NÉmeti &T. Sayed Ahmed -1997 -Bulletin of Symbolic Logic 3 (2):249.Export citation Bookmark
- On tarski’s axiomatic foundations of the calculus of relations.Hajnal Andréka,Steven Givant,Peter Jipsen &István Németi -2017 -Journal of Symbolic Logic 82 (3):966-994.It is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, (...) is derivable from the other axioms. The set of remaining axioms is independent. Finally, it is shown that if both the left-hand and right-hand distributive laws for relative multiplication are included in the set of axioms, then two of Tarski’s other axioms become redundant, namely the second involution law and the distributive law for converse. The set of remaining axioms is independent and equivalent to Tarski’s axiom system. (shrink)
- On universal algebraic logic and cylindric algebras.Hajnal Andréka &István Németi -1978 -Bulletin of the Section of Logic 7 (4):152-158.
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David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Area Editors:
David Bourget
Gwen Bradford
Berit Brogaard
Margaret Cameron
David Chalmers
James Chase
Rafael De Clercq
Ezio Di Nucci
Esa Diaz-Leon
Barry Hallen
Hans Halvorson
Jonathan Ichikawa
Monte Johnson
Michelle Kosch
Øystein Linnebo
Paul Livingston
Brandon Look
Manolo Martínez
Matthew McGrath
Michiru Nagatsu
Susana Nuccetelli
Giuseppe Primiero
Jack Alan Reynolds
Darrell P. Rowbottom
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