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

100%

Salibra A., Scollo G.

Banach Center Publications

1993

tom 28

nr 1

67-94

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 of the classical, object-oriented notions of compactness. Furthermore, a notion of cardinal pre-institution is introduced, and a Löwenheim-Skolem preservation theorem for cardinal pre-institutions is presented.

Polyadic algebras over nonclassical logics

100%

Pigozzi D., Salibra A.

Banach Center Publications

1993

tom 28

nr 1

51-66

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)'s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.

Ograniczanie wyników

2 Banach Center Publications

2 Salibra A.

1 Pigozzi D.

1 Scollo G.

2 1993

Wyniki wyszukiwania

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

Polyadic algebras over nonclassical logics