Finiteness Axioms on Fragments of Intuitionistic Set Theory
نویسندگان
چکیده
منابع مشابه
Finiteness Axioms on Fragments of Intuitionistic Set Theory
Abstract. It is proved that in a suitable intuitionistic, locally classical, version of the theory ZFC deprived of the axiom of infinity, the requirement that every set be finite is equivalent to the assertion that every ordinal is a natural number. Moreover, the theory obtained with the addition of these finiteness assumptions is equivalent to a theory of hereditarily finite sets, developed in...
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If T is a complete theory stronger than ZFFin such that axiom of extensionality for classes + T + (9X) i is consistent for 1 i k (each alone), where i are normal formulae then we showAST + (9X) 1+ +(9X) k + scheme of choice is consistent. As a consequence we get: there is no proper 1-formula inAST + scheme of choice. Moreover the complexity of the axioms of AST is studied, e.g. we show axiom of...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2007
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1193667705