منابع مشابه
Strong Axioms of Infinity and Elementary Embeddings
This is the expository paper on strong axioms of infinity and elementary embeddings origi;,ally to have been authored by Reinhardt and Solovay. It has been owed for some time and already cited with some frequency in the most recent set theoretical literature. However, for various reasons the paper did not appear in print far several years. The impetus for actual publication came from a series o...
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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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The development of axiomatic set theory originated from the need for a rigorous investigation of the basic principles at the foundations of mathematics. The classical theory of sets ZFC offers a rich framework, nevertheless many crucial problems (such as the famous continuum hypothesis) cannot be solved within this theory. For this reason, set theorists have been exploring new axioms that would...
متن کاملPartial Universes and the Axioms of Set Theory
This paper is intended as a senior thesis. The topic is set theory. The material covered is not particularly advanced with respect to the field. However, this author has never had the opportunity to take an official class in set theory; it was in the course of preparing this document that he himself was introduced to set theory. After introducing some fundamental notions from set theory and log...
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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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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1961
ISSN: 0025-5645
DOI: 10.2969/jmsj/01330220