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A note on an alleged proof of the relative consistency of P=NP with PA

2000/07/05 by Ralf Schindler, Schindler, Ralf
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.math/0007025

4 pages

openalex publication_date 2000/07/05 · arxiv created 2000/07/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We indicate that an argument of da Costa and Doria in fact proves P=NP. This observation makes their argument appear dubious. We isolate a weak version of one of their lemmas which would already prove P=NP. We point out that even this weak version is probably false. In fact, a generalized form of this weak version is provably false.

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