Some Infinitary Paradoxes and Undecidable Sentences in Peano Arithmetic
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.
math.LO↗