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Weakly atomic-compact relational structures

Published online by Cambridge University Press:  12 March 2014

G. Fuhrken  and
W. Taylor
G. Fuhrken
Affiliation:
University of Minnesota, Minneapolis, Minnesota 55455
W. Taylor
Affiliation:
University of Colorado, Boulder, Colorado 80302
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Extract

A relational structure is called weakly atomic-compact if and only if every set Σ of atomic formulas (taken from the first-order language of the similarity type of augmented by a possibly uncountable set of additional variables as “unknowns”) is satisfiable in whenever every finite subset of Σ is so satisfiable. This notion (as well as some related ones which will be mentioned in §4) was introduced by J. Mycielski as a generalization to model theory of I. Kaplansky's notion of an algebraically compact Abelian group (cf. [5], [7], [1], [8]).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 1 , March 1971 , pp. 129 - 140
Copyright
Copyright © Association for Symbolic Logic 1971

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