Displaying similar documents to “On problems of databases over a fixed infinite universe”

Order with successors is not interprétable in RCF

S. Świerczkowski (1993)

Fundamenta Mathematicae

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Using the monotonicity theorem of L. van den Dries for RCF-definable real functions, and a further result of that author about RCF-definable equivalence relations on ℝ, we show that the theory of order with successors is not interpretable in the theory RCF. This confirms a conjecture by J. Mycielski, P. Pudlák and A. Stern.

Symbol Declarations in Mathematical Writing

Wolska, Magdalena, Grigore, Mihai

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We present three corpus-based studies on symbol declaration in mathematical writing. We focus on simple object denoting symbols which may be part of larger expressions. We look into whether the symbols are explicitly introduced into the discourse and whether the information on once interpreted symbols can be used to interpret structurally related symbols. Our goal is to support fine-grained semantic interpretation of simple and complex mathematical expressions. The results of our analysis...

The Gödel Completeness Theorem for Uncountable Languages

Julian J. Schlöder, Peter Koepke (2012)

Formalized Mathematics

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This article is the second in a series of two Mizar articles constituting a formal proof of the Gödel Completeness theorem [15] for uncountably large languages. We follow the proof given in [16]. The present article contains the techniques required to expand a theory such that the expanded theory contains witnesses and is negation faithful. Then the completeness theorem follows immediately.

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.

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.

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...

Some decidable theories with finitely many covers which are decidable and algorithmically found

Cornelia Kalfa (1994)

Colloquium Mathematicae

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In any recursive algebraic language, I find an interval of the lattice of equational theories, every element of which has finitely many covers. With every finite set of equations of this language, an equational theory of this interval is associated, which is decidable with decidable covers that can be algorithmically found. If the language is finite, both this theory and its covers are finitely based. Also, for every finite language and for every natural number n, I construct a finitely...

A new interpretor for PARI/GP

Bill Allombert (2008)

Journal de Théorie des Nombres de Bordeaux

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When Henri Cohen and his coworkers set out to write PARI twenty years ago, GP was an afterthought. While GP has become the most commonly used interface to the PARI library by a large margin, both the gp interpretor and the GP language are primitive in design. Paradoxically, while gp allows to handle very high-level objects, GP itself is a low-level language coming straight from the seventies. We rewrote GP as a compiler/evaluator pair, implementing several high-level features...