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Some Infinitary Paradoxes and Undecidable Sentences in Peano Arithmetic

2016/04/12 by Ka-Yue Cheng, Cheng, Ka-Yue
Computer Science · Psychology · #03F40 #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Philosophy and Theoretical Science

paper · pdf · doi:10.48550/arxiv.1604.03452

openalex publication_date 2016/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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