Movatterモバイル変換

[0]ホーム
URL:

PhilPapersPhilPeoplePhilArchivePhilEventsPhilJobs

Works by A. S. Troelstra

(view other items matching `A. S. Troelstra`,view all matches )
35 found
Order:

1 filter applied
  1.  62
    Constructivism in Mathematics: An Introduction.A. S. Troelstra &Dirk Van Dalen -1988 - Amsterdam: North Holland. Edited by D. van Dalen.
    The present volume is intended as an all-round introduction to constructivism. Here constructivism is to be understood in the wide sense, and covers in particular Brouwer's intuitionism, Bishop's constructivism and A.A. Markov's constructive recursive mathematics. The ending "-ism" has ideological overtones: "constructive mathematics is the (only) right mathematics"; we hasten, however, to declare that we do not subscribe to this ideology, and that we do not intend to present our material on such a basis.
    Direct download  
     
    Export citation  
     
    Bookmark   176 citations  
  2.  61
    Note on the Fan theorem.A. S. Troelstra -1974 -Journal of Symbolic Logic 39 (3):584-596.
  3.  42
    Realizability.A. S. Troelstra -2000 -Bulletin of Symbolic Logic 6 (4):470-471.
  4.  95
    Realizability and intuitionistic logic.J. Diller &A. S. Troelstra -1984 -Synthese 60 (2):253 - 282.
  5.  71
    Analysing choice sequences.A. S. Troelstra -1983 -Journal of Philosophical Logic 12 (2):197 - 260.
  6. Projections of lawless sequences.D. Van Dalen &A. S. Troelstra -1970 - In A. Kino, John Myhill & Richard Eugene Vesley,Intuitionism and proof theory. Amsterdam,: North-Holland Pub. Co..
  7.  39
    Natural deduction for intuitionistic linear logic.A. S. Troelstra -1995 -Annals of Pure and Applied Logic 73 (1):79-108.
    The paper deals with two versions of the fragment with unit, tensor, linear implication and storage operator of intuitionistic linear logic. The first version, ILL, appears in a paper by Benton, Bierman, Hyland and de Paiva; the second one, ILL+, is described in this paper. ILL has a contraction rule and an introduction rule !I for the exponential; in ILL+, instead of a contraction rule, multiple occurrences of labels for assumptions are permitted under certain conditions; moreover, there is a different (...) introduction rule for the exponential, !I+, which is closer in spirit to the necessitation rule for the normalizable version of S4 discussed by Prawitz in his monograph “Natural Deduction”.It is relatively easy to adapt Prawitz's treatment of natural deduction for intuitionistic logic to ILL+; in particular one can formulate a notion of strong validity permitting a proof of strong normalization.The conversion rules for ILL explicitly mentioned in the paper by Benton et al. do not suffice for normal forms with subformula property, but we can show that this can be remedied by addition of a special permutation conversion plus some “satellite” permutation conversions.Some discussion of the categorical models which might correspond to ILL+ is given. (shrink)
    Direct download(4 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  8. (1 other version)Basic proof theory.A. S. Troelstra -1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.
     
    Export citation  
     
    Bookmark   5 citations  
  9.  255
    Some models for intuitionistic finite type arithmetic with Fan functional.A. S. Troelstra -1977 -Journal of Symbolic Logic 42 (2):194-202.
    In this note we shall assume acquaintance with [T4] and the parts of [T1] which deal with intuitionistic arithmetic in all finite types. The bibliography just continues the bibliography of [T4].The principal purpose of this note is the discussion of two models for intuitionistic finite type arithmetic with fan functional. The first model is needed to correct an oversight in the proof of Theorem 6 [T4, §5]: the model ECF+as defined there cannot be shown to have the required properties inEL+ (...) QF-AC, the reason being that a change in the definition ofW12alone does not suffice—if one wishes to establish closure under the operations of HAωthe definitions ofW1σfor other σ have to be adopted as well. It is difficult to see how to do this directly in a uniform way — but we succeed via a detour, which is described in §2.For a proper understanding, we should perhaps note already here thaton the assumption of the fan theorem, ECF+as defined in [T4] and the new model of this note coincide ; but inELit is impossible to prove this. (shrink)
    Direct download(8 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  10.  70
    On a second order propositional operator in intuitionistic logic.A. S. Troelstra -1981 -Studia Logica 40 (2):113 - 139.
    This paper studies, by way of an example, the intuitionistic propositional connective * defined in the language of second order propositional logic by. In full topological models * is not generally definable, but over Cantor-space and the reals it can be classically shown that; on the other hand, this is false constructively, i.e. a contradiction with Church's thesis is obtained. This is comparable with some well-known results on the completeness of intuitionistic first-order predicate logic.Over [0, 1], the operator * is (...) (constructively and classically) undefinable. We show how to recast this argument in terms of intuitive intuitionistic validity in some parameter. The undefinability argument essentially uses the connectedness of [0, 1]; most of the work of recasting consists in the choice of a suitable intuitionistically meaningful parameter, so as to imitate the effect of connectedness. (shrink)
    Direct download(4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  11. Construction in Mathematics. An Introduction, Volume 1.A. S. Troelstra &D. van Dalen -1990 -Studia Logica 49 (1):151-152.
  12.  73
    Choice sequences and informal rigour.A. S. Troelstra -1985 -Synthese 62 (2):217 - 227.
    In this paper we discuss a particular example of the passage from the informal, but rigorous description of a concept to the axiomatic formulation of principles holding for the concept; in particular, we look at the principles of continuity and lawlike choice in the theory of lawless sequences. Our discussion also leads to a better understanding of the rôle of the so-called density axiom for lawless sequences.
    Direct download(4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  13.  44
    Informal theory of choice sequences.A. S. Troelstra -1969 -Studia Logica 25 (1):31 - 54.
  14.  15
    The Theory of Choice Sequences.A. S. Troelstra,B. van Rootselaar &J. F. Staal -1973 -Journal of Symbolic Logic 38 (2):332-332.
  15.  56
    Concepts and Axioms.A. S. Troelstra -1998 -Philosophia Mathematica 6 (2):195-208.
    The paper discusses the transition from informal concepts to mathematically precise notions; examples are given, and in some detail the case of lawless sequences, a concept of intuitionistic mathematics, is discussed. A final section comments on philosophical discussions concerning intuitionistic logic in connection with a ‘theory of meaning’.
    Direct download(8 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  16.  42
    Strong normalization for typed terms with surjective pairing.A. S. Troelstra -1986 -Notre Dame Journal of Formal Logic 27 (4):547-550.
    Direct download(4 more)  
     
    Export citation  
     
    Bookmark  
  17.  20
    The L.E.J. Brouwer Centenary Symposium: proceedings of the conference held in Noordwijkerhout, 8-13 June 1981.L. E. J. Brouwer,A. S. Troelstra &D. van Dalen (eds.) -1982 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co..
  18.  20
    An Interpretation of the Intuitionistic Propositional Calculus.John Dawson &A. S. Troelstra -1990 -Journal of Symbolic Logic 55 (1):346-346.
  19.  32
    On the Intuitionistic Propositional Calculus.John Dawson &A. S. Troelstra -1990 -Journal of Symbolic Logic 55 (1):344-344.
  20. [Omega]-Bibliography of Mathematical Logic.G. H. Müller,Wolfgang Lenski,Jane E. Kister,D. van Dalen &A. S. Troelstra -1987
     
    Export citation  
     
    Bookmark  
  21.  31
    An addendum.A. S. Troelstra -1971 -Annals of Mathematical Logic 3 (4):437.
  22. Constructivism in Mathematics, Volume 2.A. S. Troelstra &D. van Dalen -1991 -Studia Logica 50 (2):355-356.
  23. History of Constructivism in the 20th Century Vol. Ml-91-05.A. S. Troelstra -1991 - University of Amsterdam.
  24.  52
    Marginalia on sequent calculi.A. S. Troelstra -1999 -Studia Logica 62 (2):291-303.
    The paper discusses the relationship between normal natural deductions and cutfree proofs in Gentzen (sequent) calculi in the absence of term labeling. For Gentzen calculi this is the usual version; for natural deduction this is the version under the complete discharge convention, where open assumptions are always discharged as soon as possible. The paper supplements work by Mints, Pinto, Dyckhoff, and Schwichtenberg on the labeled calculi.
    Direct download(5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  25.  43
    Nieformalna teoria ciągów Z wyboru.A. S. Troelstra -1969 -Studia Logica 25 (1):53-53.
  26. The Discovery of E.W. Beth’s Semantics for Intuitionistic Logic.A. S. Troelstra &P. van Ulsen -1999 - In Jelle Gerbrandy, Maarten Marx, Maarten de Rijke & Yde Venema,Essays dedicated to Johan van Benthem on the occasion of his 50th birthday. Amsterdam University Press.
     
    Export citation  
     
    Bookmark   1 citation  
  27.  27
    Toshio Umezawa. On logics intermediate between intuitionistic and classical predicate logic. The journal of symbolic logic, vol. 24 no. 2 , pp. 141–153.A. S. Troelstra -1969 -Journal of Symbolic Logic 33 (4):607.
  28. Logic and foundations of mathematics.D. van Dalen,J. G. Dijkman,A. Heyting,Stephen Cole Kleene &A. S. Troelstra (eds.) -1969 - Groningen,: Wolters-Noordhoff.
  29.  65
    Feferman Solomon. A language and axioms for explicit mathematics. Algebra and logic, Papers from the 1974 Summer Research Institute of the Australian Mathematical Society, Monash University, Australia, edited by Crossley J. N., Lecture notes in mathematics, vol. 450, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 87–139.Feferman Solomon. Constructive theories of functions and classes. Logic colloquium '78, Proceedings of the colloquium held in Mons, August 1978, edited by Boffa Maurice, van Dalen Dirk, and McAloon Kenneth, Studies in logic and the foundations of mathematics, vol. 97, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1979, pp. 159–224. [REVIEW]G. R. Renardel de Lavalette &A. S. Troelstra -1984 -Journal of Symbolic Logic 49 (1):308-311.
  30.  54
    Review: A. G. Dragalin, E. Mendelson, Mathematical Intuitionism. Introduction to Proof Theory. [REVIEW]A. S. Troelstra -1990 -Journal of Symbolic Logic 55 (3):1308-1309.
  31.  46
    Mariko Yasugi. Intuitionistic analysis and Gödel's interpretation. Journal of the Mathematical Society of Japan, vol. 15 , pp. 101–112. [REVIEW]A. S. Troelstra -1972 -Journal of Symbolic Logic 37 (2):404.
  32.  33
    Nagashima Takashi. An extension of the Craig-Schütte interpolation theorem. Annals of the Japan Association for Philosophy of Science, vol. 3 no. 1 , pp. 12–18. [REVIEW]A. S. Troelstra -1968 -Journal of Symbolic Logic 33 (2):291-292.
  33.  28
    (1 other version)Review: Bruno Scarpellini, Proof Theory and Intuitionistic Systems. [REVIEW]A. S. Troelstra -1974 -Journal of Symbolic Logic 39 (3):607-609.
  34.  15
    Review: Toshio Umezawa, On Logics Intermediate Between Intuitionistic and Classical Predicate Logic. [REVIEW]A. S. Troelstra -1968 -Journal of Symbolic Logic 33 (4):607-607.
  35.  54
    Tsutomu Hosoi. On intermediate logics. Journal of the Faculty of Science, University of Tokyo, section I, vol. 14 , pp. 293–312, and vol. 16 , pp. 1–12. [REVIEW]A. S. Troelstra -1971 -Journal of Symbolic Logic 36 (2):329-330.
    Direct download(3 more)  
     
    Export citation  
     
    Bookmark  
Export
Limit to items.
Filters





Configure languageshere.Sign in to use this feature.

Viewing options


Open Category Editor
Off-campus access
Using PhilPapers from home?

Create an account to enable off-campus access through your institution's proxy server or OpenAthens.

Monitor this page
Be alerted of all new items appearing on this page. Choose how you want to monitor it:

Email RSS feed
Home |New books and articles |Bibliographies |Philosophy journals |About PhilPapers |API |Contact us |Code of conduct

CDPPhiosophy Documentation Center
PhilPapers logo byAndrea Andrews andMeghan Driscoll.
This site uses cookies and Google Analytics (see ourterms & conditions for details regarding the privacy implications).

Use of this site is subject toterms & conditions.
All rights reserved byThe PhilPapers Foundation

Server: philpapers-web-54b44b69b7-nwt9g uwo
[8]ページ先頭
©2009-2025 Movatter.jp