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

Antonino Salibra, Giuseppe Scollo (1993)

Banach Center Publications

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 generalizations...

Deciding whether a relation defined in Presburger logic can be defined in weaker logics

Christian Choffrut (2008)

RAIRO - Theoretical Informatics and Applications

We consider logics on and which are weaker than Presburger arithmetic and we settle the following decision problem: given a k-ary relation on and which are first order definable in Presburger arithmetic, are they definable in these weaker logics? These logics, intuitively, are obtained by considering modulo and threshold counting predicates for differences of two variables.

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