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

Tom 28 / 1993

Antonino Salibra, Giuseppe Scollo Banach Center Publications 28 (1993), 67-94 DOI: 10.4064/-28-1-67-94


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.


  • Antonino Salibra
  • Giuseppe Scollo

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