TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY
TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY
复制标题
副一致性集合论中的超限数
DOI：
10.1017/s1755020309990281
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Z. Weber
中科院分区：
文献类型：
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作者：
Z. Weber
本文开始了朴素集合论的公理化发展——完全理解原理的后果——在次一致逻辑中。结果分为两类。经典重演证明了序数和皮亚诺算术的主要定理，表明朴素集合论可以为标准数学提供基础。然后还有主要的扩展，包括著名悖论和选择公理（以良序原理的形式）的证明。最后，我指出基数的后来发展将如何导致康托定理、大基数的存在以及连续统假设的反例。
This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis.