Topological representations of Post algebras of order ω+and open theories based on ω+-valued Post logic
✍ Scribed by Helena Rasiowa
- Publisher
- Springer Netherlands
- Year
- 1985
- Tongue
- English
- Weight
- 834 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0039-3215
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✦ Synopsis
Post algebras of order r as a semantic foundation for o~+.valued predicate calculi were examined in [5]. In this paper Post spaces of order r being a modification of Post spaces of order ~> 2 (cf. Traczyk [8],Dwinger [1],Rasiowa [6]) are introduced and Post fields of order r are defined, i representation theorem for Post algebras of order co + 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 estabilshed and applied to Lindenbaum-Tarski algebras of elementary theories based on r predicate calculi in order to obtain a topological characterization of open theories.