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Interpolation and compactness in categories of pre-institutions

Published online by Cambridge University Press:  04 March 2009

Antonino Salibra  and
Giuseppe Scollo
Antonino Salibra
Affiliation:
University of Venice, Dip. Matematica Applicata e Informatica Via Torino 155, 1–30173 Venezia, Italy Email [email protected]
Giuseppe Scollo
Affiliation:
University of Twente, Fac. Informatica PO Box 211, NL-7500AE Enschede, The Netherlands Email [email protected]
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Abstract

An analysis of relationships between Craig-style interpolation, compactness, and other related model-theoretic properties is carried out in the softer framework of categories of pre-institutions. While the equivalence between sentence interpolation and the Robinson property under compactness and Boolean closure is well known, a similar result under different assumptions (not involving compactness) is newly established for presentation interpolation. The standard concept of naturality of model transformation is enriched by a new property, termed restriction adequacy, which proves useful for the reduction of interpolation along pre-institution transformations. A distinct reduction theorem for the Robinson property is presented as well. A variant of the ultraproduct concept is further introduced, and the related closure property for pre-institutions is shown to be equivalent to compactness

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 3 , June 1996 , pp. 261 - 286
Copyright
Copyright © Cambridge University Press 1996

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