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arXiv · 1604.03452

Some Infinitary Paradoxes and Undecidable Sentences in Peano Arithmetic

Ka-Yue Cheng
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Abstract

According to Chaitin, Gödel once told him "it doesn't matter which paradox you use [to prove the First Incompleteness Theorem]". In this paper I will present a few infinitary paradoxes and show how to "translate" them to some undecidable sentences in Peano arithmetic, like what Gödel did to the Liar paradox. The results partly verify Gödel's claim.

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BibTeXRIS

Ka-Yue Cheng. 2016-04-12. Some Infinitary Paradoxes and Undecidable Sentences in Peano Arithmetic. https://arxiv.org/abs/1604.03452

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