Displaying similar documents to “The Gödel Completeness Theorem for Uncountable Languages”

Transition of Consistency and Satisfiability under Language Extensions

Julian J. Schlöder, Peter Koepke (2012)

Formalized Mathematics

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This article is the first in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [17] for uncountably large languages. We follow the proof given in [18]. The present article contains the techniques required to expand formal languages. We prove that consistent or satisfiable theories retain these properties under changes to the language they are formulated in.

Sequent Calculus, Derivability, Provability. Gödel's Completeness Theorem

Marco Caminati (2011)

Formalized Mathematics

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Fifth of a series of articles laying down the bases for classical first order model theory. This paper presents multiple themes: first it introduces sequents, rules and sets of rules for a first order language L as L-dependent types. Then defines derivability and provability according to a set of rules, and gives several technical lemmas binding all those concepts. Following that, it introduces a fixed set D of derivation rules, and proceeds to convert them to Mizar functorial cluster...

Strong completeness of the Lambek Calculus with respect to Relational Semantics

Szabolcs Mikulás (1993)

Banach Center Publications

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In [vB88], Johan van Benthem introduces Relational Semantics (RelSem for short), and states Soundness Theorem for Lambek Calculus (LC) w.r.t. RelSem. After doing this, he writes: "it would be very interesting to have the converse too", i.e., to have Completeness Theorem. The same question is in [vB91, p. 235]. In the following, we state Strong Completeness Theorems for different versions of LC.

The Derivations of Temporal Logic Formulas

Mariusz Giero (2012)

Formalized Mathematics

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This is a preliminary article to prove the completeness theorem of an extension of basic propositional temporal logic. We base it on the proof of completeness for basic propositional temporal logic given in [12]. We introduce n-ary connectives and prove their properties. We derive temporal logic formulas.

Construction of sentences with specific interpretability properties

A. Stern (1993)

Fundamenta Mathematicae

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The Rowland Institute for Science, 100 Cambridge Parkway, Cambridge, Massachusetts 02142, U.S.A. A construction is presented for generating sentences that satisfy a recursively enumerable set of interpretability properties. This construction is then used to prove three previously announced results concerning the lattice of local interpretability types of theories (also known as the Lattice of Chapters).

Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms

Marco Caminati (2011)

Formalized Mathematics

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Second of a series of articles laying down the bases for classical first order model theory. A language is defined basically as a tuple made of an integer-valued function (adicity), a symbol of equality and a symbol for the NOR logical connective. The only requests for this tuple to be a language is that the value of the adicity in = is -2 and that its preimage (i.e. the variables set) in 0 is infinite. Existential quantification will be rendered (see [11]) by mere prefixing a formula...

First Order Languages: Further Syntax and Semantics

Marco Caminati (2011)

Formalized Mathematics

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Third of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a consequence, the evaluation of any w.f.f. string and the relation of logical implication are...

Strong normalization proofs for cut elimination in Gentzen's sequent calculi

Elias Bittar (1999)

Banach Center Publications

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We define an equivalent variant L K s p of the Gentzen sequent calculus L K . In L K s p weakenings or contractions can be performed in parallel. This modification allows us to interpret a symmetrical system of mix elimination rules L K s p by a finite rewriting system; the termination of this rewriting system can be machine checked. We give also a self-contained strong normalization proof by structural induction. We give another strong normalization proof by a strictly monotone subrecursive interpretation;...