Set Theory and Logic


Refutation of the Halting Problem: not a Problem

Authors: Colin James III

Alan Turing's difficulty was in expressing the halting problem in the format of a two-valued logic which was not as expressive as in a four-valued logic to show nuances of what exactly the equation stated. In comparison to Gödel's incompleteness theorems, Turing's halting problem has no superficial similarities other than being refuted as not a problem. Hence in contrast, both expressions are disparate and ultimately unrelated as to content meaning. Therefore: The assumption that there is a consistent and complete axiomatization of all true first-order logic statements about natural numbers must be tautologous.

Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved.

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[v1] 2018-01-16 09:29:47

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