Connecting the provable with the unprovable: phase transitions for unprovability
Florian Pelupessy · Ghent University Academic Bibliography (Ghent University) · 2012
Why are some theorems not provable in certain theories of mathematics? Why are most theorems from existing mathematics provable in very weak systems? Unprovability theory seeks answers for those questions. Logicians have obtained unprovable statements which resemble provable statements. These statements often contain some condition which seems to cause unprovability, as this condition can be modified, using a function parameter, in such a manner as to make the theorem provable. It turns out that in many cases there is a phase transition: By modifying the parameter slightly one changes the theorem from provable to unprovable. We study these transitions with the goal of gaining more insights into unprovability.