A Stronger Foundation for Computer Science and P=NP

Mark Inman

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arXiv · 1708.05714

A Stronger Foundation for Computer Science and P=NP

Mark Inman

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Abstract

This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which decides over $\beta^{'}$ implies inconsistency in ZFC. We then discover that unrestricted use of the axiom of substitution can lead to hidden assumptions in a certain class of proofs by contradiction. These hidden assumptions create an implied axiom of incompleteness for ZFC. Later, we offer a restriction on the axiom of substitution by introducing a new axiom which prevents impredicative tautologies from producing theorems. Our discovery in regards to these foundational arguments, disproves the SPACE hierarchy theorem which allows us to solve the P vs NP problem using a TIME-SPACE equivalence oracle.

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BibTeX RIS

Mark Inman. 2017-08-18. A Stronger Foundation for Computer Science and P=NP. https://arxiv.org/abs/1708.05714

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