Topological representations of post algebras of order ω+ and open theories based on ω+-valued post logic

Studia Logica 44 (4):353 - 368 (1985)
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Abstract

Post algebras of order + as a semantic foundation for +-valued predicate calculi were examined in [5]. In this paper Post spaces of order + being a modification of Post spaces of order n2 (cf. Traczyk [8], Dwinger [1], Rasiowa [6]) are introduced and Post fields of order + are defined. A representation theorem for Post algebras of order + as Post fields of sets is proved. Moreover necessary and sufficient conditions for the existence of representations preserving a given set of infinite joins and infinite meets are established and applied to Lindenbaum-Tarski algebras of elementary theories based on +-valued predicate calculi in order to obtain a topological characterization of open theories.

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