Corcoran's Aristotelian syllogistic as a subsystem of first-order logic.
Andrade, Edgar J., Becerra, Edward (2007)
Revista Colombiana de Matemáticas
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Andrade, Edgar J., Becerra, Edward (2007)
Revista Colombiana de Matemáticas
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Casanovas, Enrique (2007)
Revista Colombiana de Matemáticas
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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.
Grulović, Milan Z. (2002)
Novi Sad Journal of Mathematics
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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.
Tatjana Stojanović, Ana Kaplarević-Mališić, Zoran Ognjanović (2010)
Kragujevac Journal of Mathematics
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Vladimir Ristić (2006)
Kragujevac Journal of Mathematics
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A. Simon (1993)
Banach Center Publications
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Freyd, Peter (2008)
Theory and Applications of Categories [electronic only]
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Tetruashvili, M. (1994)
Georgian Mathematical Journal
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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...
Buzykaeva, A.N. (2002)
Sibirskij Matematicheskij Zhurnal
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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.
Elias Bittar (1999)
Banach Center Publications
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We define an equivalent variant of the Gentzen sequent calculus . In weakenings or contractions can be performed in parallel. This modification allows us to interpret a symmetrical system of mix elimination rules 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;...