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arXiv math/03052822003-05-19math.LO

自指Parases、不完全性和不动点的一种通用方法

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points

Noson S. Yanofsky

发表信息：: The Bulletin of Symbolic Logic, Vol 9, 2003, NUMBER = 3, PAGES = 362--386
DOI：: 10.2178/bsl/1058448677

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摘要：

继F. WilliamLawvere，我们证明了许多自指悖论，不完全性定理和不动点定理都来自同一个简单的方案。我们展示了这些相似之处，通过展示这个简单的方案如何包含语义悖论，以及它们如何在逻辑，可计算性理论，复杂性理论和形式语言理论中作为对角线方法和不动点定理出现。

英文摘要：

Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.

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