Displaying similar documents to “Construction of sentences with specific interpretability properties”

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.

Arithmetical transfinite induction and hierarchies of functions

Z. Ratajczyk (1992)

Fundamenta Mathematicae

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We generalize to the case of arithmetical transfinite induction the following three theorems for PA: the Wainer Theorem, the Paris-Harrington Theorem, and a version of the Solovay-Ketonen Theorem. We give uniform proofs using combinatorial constructions.

Compactness and Löwenheim-Skolem properties in categories of pre-institutions

Antonino Salibra, Giuseppe Scollo (1993)

Banach Center Publications

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The abstract model-theoretic concepts of compactness and Löwenheim-Skolem properties are investigated in the "softer" framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institution. These results rely on notions of compact transformation, which are introduced as arrow-oriented...

Beta-reduction as unification

A. Kfoury (1999)

Banach Center Publications

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We define a new unification problem, which we call β-unification and which can be used to characterize the β-strong normalization of terms in the λ-calculus. We prove the undecidability of β-unification, its connection with the system of intersection types, and several of its basic properties.

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;...