Some Infinitary Paradoxes and Undecidable Sentences in Peano Arithmetic
Ka-Yue Cheng · arXiv (Cornell University) · 2016
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.