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Constructibility in higher order arithmetics

Archive for Mathematical Logic 32 (6):381-389 (1993)

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Interpretations of the alternative set theory.A. Sochor - 1993 - Archive for Mathematical Logic 32 (6):391-398.details We show an axiom A such that there is no nontrivial interpretation of the alternative set theory (AST) inAST+A keeping ∈, sets and the class of all “standard” natural numbers. Furthermore, there is no interpretation ofAST inAST without the prolongation axiom, but there is an interpretation ofAST in the theory having the prolongation axiom and the basic set-theoretical axioms only. Download Export citation Bookmark 2 citations
Choices of Convenient Sets.Antonín Sochor - 1994 - Mathematical Logic Quarterly 40 (1):51-60.details Proceeding in the theory with extensionality, comprehension for classes, existence of the empty set and the assumption the addition of one element to a set makes again a set we show a week assumption which guarantees existence of a saturated elementary extension of the system of hereditarily finite sets. Download Export citation Bookmark 1 citation

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