The P versus NP problem is addressed in a context of provability and limitations on the possibility of finding sound axioms for formal theories. We construct a particular family D of decision problems and show that D necessarily contains a problem which is in NP. Further, it is shown that if the term ``constructible theory'' is defined by a specific natural condition, then no constructible and sound formal theory can prove membership in P for any of the decision problems in D.

翻译：暂无翻译