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

Antonino Salibra; Giuseppe Scollo

Banach Center Publications (1993)

  • Volume: 28, Issue: 1, page 67-94
  • ISSN: 0137-6934

Abstract

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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 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.

How to cite

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Salibra, Antonino, and Scollo, Giuseppe. "Compactness and Löwenheim-Skolem properties in categories of pre-institutions." Banach Center Publications 28.1 (1993): 67-94. <http://eudml.org/doc/262664>.

@article{Salibra1993,
abstract = {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.},
author = {Salibra, Antonino, Scollo, Giuseppe},
journal = {Banach Center Publications},
keywords = {abstract logics; compactness; pre-institutions; Löwenheim-Skolem theorem},
language = {eng},
number = {1},
pages = {67-94},
title = {Compactness and Löwenheim-Skolem properties in categories of pre-institutions},
url = {http://eudml.org/doc/262664},
volume = {28},
year = {1993},
}

TY - JOUR
AU - Salibra, Antonino
AU - Scollo, Giuseppe
TI - Compactness and Löwenheim-Skolem properties in categories of pre-institutions
JO - Banach Center Publications
PY - 1993
VL - 28
IS - 1
SP - 67
EP - 94
AB - 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.
LA - eng
KW - abstract logics; compactness; pre-institutions; Löwenheim-Skolem theorem
UR - http://eudml.org/doc/262664
ER -

References

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