I would like to ask this:
- Does anybody know about some kind of paper/analysis/research/thesis/etc. which examines that whether there is any connection between the P = NP problem and accepting the Axiom of Choice as true or false (and use ZF+AC or ZF+$\neg$AC) or not?
I ask this question because recently I read the wikipedia page of the Axiom of Choice and found this in the section called "Statements consistent with the negation of AC":
...For certain models of ZF+$\neg$AC, it is possible to prove the negation of some standard facts... There exists a model of ZF+$\neg$AC in which real numbers are a countable union of countable sets
So, for me this means that it is possible that emerging of the cardinality of the continuum is based on we accept the Axiom of Choice as true or false. In that case is there any chance for the truthfullness of P = NP is based on how we accept the Axiom of Choice as well?
Thx for any reply!