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Some Infinitary Paradoxes and Undecidable Sentences in Peano Arithmetic
Preprint
2016-04-12
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Abstract
According to Chaitin, G\"odel 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 G\"odel did to the Liar paradox. The results partly verify G\"odel's claim.