In formal theories oftruth, atruth predicate is a fundamental concept based on thesentences of aformal language as interpreted logically. That is, it formalizes the concept that is normally expressed by saying that a sentence, statement or idea "is true."
Based on "Chomsky Definition", a language is assumed to be acountable set of sentences, each of finite length, and constructed out of a countable set of symbols. A theory of syntax is assumed to introduce symbols, and rules to constructwell-formed sentences. A language is called fully interpreted if meanings are attached to its sentences so that they all are either true or false.
A fully interpreted languageL which does not have a truth predicate can be extended to a fully interpreted languageĽthat contains a truth predicateT, i.e., the sentenceA ↔T(⌈A⌉) is true for every sentenceA ofĽ, whereT(⌈A⌉) stands for "the sentence (denoted by)A is true". The main tools to prove this result areordinary andtransfinite induction, recursion methods, andZF set theory (cf.[1] and[2]).
| General | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Theorems (list) and paradoxes | |||||||||
| Logics |
| ||||||||
| Set theory |
| ||||||||
| Formal systems (list), language and syntax |
| ||||||||
| Proof theory | |||||||||
| Model theory | |||||||||
| Computability theory | |||||||||
| Related | |||||||||
 | Thislinguistics article is astub. You can help Wikipedia byexpanding it. |
