A Theory That Proves Its Own Inconsistency · Yan Sheng's site
I recently read this mind-bending blog post by Joel David Hamkins that proves this result: there is a Turing machine program P P such that for any function f:N→N f:N→N—possibly uncomputable!—there is a model of Peano arithmetic (PA) in which P P computes f f on the standard natural numbers. If this statement doesn’t surprise you, I’m not sure what else would (except maybe those who work in logic or set theory; I’m convinced that these people routinely believe as many as six impossible things before breakfast).
A Theory That Proves Its Own Inconsistency · Yan Sheng's site Welcome to my site! © 2019. All rights reserved. Yan Sheng's site A math blog A Theory That Proves Its Own Inconsistency 06 Dec 2018 logic I recently read this mind-bending blog post by Joel David Hamkins that proves this result: there is a Turing machine program $P$ such that for any function $f:\bb N\to\bb N$—possibly uncomputable!—there is a model of Peano arithmetic (PA) in which $P$ computes $f$ on the standard natural numbers. If this statement doesn’t surprise you, I’m not sure what else would (except maybe those
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