A Stronger Foundation for Computer Science and P=NP
This addresses foundational problems in computer science and mathematics, potentially resolving P vs NP, but the claims are extreme and unverified.
The paper tackles foundational issues in computer science by constructing a Turing machine that solves an RE-complete problem, which implies inconsistency in ZFC due to undecidability, and disproves the SPACE hierarchy theorem to solve P vs NP using a TIME-SPACE equivalence oracle.
This article describes a Turing machine which can solve for $β^{'}$ 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 $β^{'}$ 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.