Definitions for complete theory
com·plete the·o·ry

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1. Complete theory

   In mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or its negation is provable. That is, for every sentence φ , {\displaystyle \varphi ,} the theory T {\displaystyle T} contains the sentence or its negation but not both (that is, either T ⊢ φ {\displaystyle T\vdash \varphi } or T ⊢ ¬ φ {\displaystyle T\vdash \neg \varphi } ). Recursively axiomatizable first-order theories that are consistent and rich enough to allow general mathematical reasoning to be formulated cannot be complete, as demonstrated by Gödel's first incompleteness theorem. This sense of complete is distinct from the notion of a complete logic, which asserts that for every theory that can be formulated in the logic, all semantically valid statements are provable theorems (for an appropriate sense of "semantically valid"). Gödel's completeness theorem is about this latter kind of completeness.

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1. Complete theory

   In mathematical logic, a theory is complete if it is a maximal consistent set of sentences, i.e., if it is consistent, and none of its proper extensions is consistent. For theories in logics which contain classical propositional logic, this is equivalent to asking that for every sentence φ in the language of the theory it contains either φ itself or its negation ¬φ. Recursively axiomatizable first-order theories that are rich enough to allow general mathematical reasoning to be formulated cannot be complete, as demonstrated by Gödel's incompleteness theorem. This sense of complete is distinct from the notion of a complete logic, which asserts that for every theory that can be formulated in the logic, all semantically valid statements are provable theorems. Gödel's completeness theorem is about this latter kind of completeness. Complete theories are closed under a number of conditions internally modelling the T-schema: ⁕For a set : if and only if and, ⁕For a set : if and only if or . Maximal consistent sets are a fundamental tool in the model theory of classical logic and modal logic. Their existence in a given case is usually a straightforward consequence of Zorn's lemma, based on the idea that a contradiction involves use of only finitely many premises. In the case of modal logics, the collection of maximal consistent sets extending a theory T can be given the structure of a model of T, called the canonical model.

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How to say complete theory in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of complete theory in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of complete theory in Pythagorean Numerology is: 9

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Complete_Theory
2. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=complete theory