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ArticleOriginal scientific text

Title

Atomic compactness for reflexive graphs

Authors 1

Affiliations

  1. Université de la Réunion 15, avenue René Cassin, BP 7151, 97715 Saint Denis Messag. Cedex 9, France

Abstract

A first order structure M with universe M is atomic compact if every system of atomic formulas with parameters in M is satisfiable in M provided each of its finite subsystems is. We consider atomic compactness for the class of reflexive (symmetric) graphs. In particular, we investigate the extent to which "sparse" graphs (i.e. graphs with "few" vertices of "high" degree) are compact with respect to systems of atomic formulas with "few" unknowns, on the one hand, and are pure restrictions of their Stone-Čech compactifications, on the other hand.

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Fundamenta Mathematicae
1999/162/2
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Pages:
99-117
Main language of publication
English
Received
1997-04-14
Accepted
1999-02-27
Published
1999
Exact and natural sciences