Set Theory and Logic

Reductiones ad Absurdum of the "P Versus NP Problem" and P = Np/ap/ch

Authors: Deng Ke
Comments: 17 Pages.

There exist latent meta-axioms concerning propositions in mathematics that are often overlooked. A discussion of these axioms simultaneously brings to light the secondarity of mathematics with respect to reality. Applying one of these axioms to the "P/NP problem" can reduce the problem to absurdity; however, precisely due to this secondarity of mathematics, such a dissolution can only ever be a "dissolution" rather than a "solution." To approach the "P/NP problem", we again adopt a reductio ad absurdum method: understanding the limitations of polynomial-time algorithms and identifying such limitations within NP-complete problems, thereby obtaining P≠NP. Extending this reductio from the specific contradiction between polynomial-time algorithms and NP-complete problems to the more general contradiction between guarantee of winning and symmetric mutually-exclusive games, we arrive, in the computational and purely logical domains respectively, at the conclusions P≠AP and P≠CH.
Category: Set Theory and Logic