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Eastern Model‐Theory for Boolean‐Valued Theories
Author(s) -
Georgescu George,
Voiculescu Iana
Publication year - 1985
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19850310109
Subject(s) - george (robot) , mathematics , computer science , artificial intelligence
In this paper we study some model-theoretic properties of Boolean-valued models in which the interpretations of certain first-order sentences have prescribed values in a fixed complete Boolean algebra ; these are models of a natural Boolean-valued analogue of a consistent first-order theory as introduced in A. SHORB’S thesis [12] (see also [7]). We obtain conditions for such a Boolean-valued theory to be preserved under submodels or under unions of chains; the conditions are in terms of the least Boolean-value which an universal, or Qhentence, respectively, has to take in a model of the given theory. These results enable us to investigate model completeness and existentially closed models for a Boolean-valued theory. It is proved that the relation between a model companion for a first-order theory and its cIass of existentially closed models still holds in this context.