Brief Introduction to Unprovability

Exact unprovability results for compound well-quasi-ordered combinatorial classes

In this paper we prove general exact unprovability results that show how a threshold between provability and unprovability of a finite well-quasi-orderedness assertion of a combinatorial class is transformed by the sequence-construction, multisetconstruction, cycle-construction and labeled-tree-construction. Provability proofs use asymptotic pigeonhole principle, unprovability proofs use Weierm...

Unprovability, phase transitions and the Riemann zeta-function

Unprovability Theory started with Kurt Gödel’s incompleteness theorems in 1931 but only gained mathematical significance since the late 1970s when Jeff Paris and Harvey Friedman discovered the first few families of interesting combinatorial statements that cannot be proved using the axioms of Peano Arithmetic or even some stronger axiomatic systems. In this survey article we briefly introduce t...

New results on unprovability and logical strength

This is a preprint for Max-Planck Institute’s proceedings. We present recent results in the area of unprovability. We find unprovable statements about a general class of functions using similtaneous diophantine approximation, unprovability results about the Riemann zeta-function using almost-periodicity and probabilistic arguments and a simple unprovability result about converging series using ...

Unprovability of Consistency Statements in

Several proofs of PA-unprovability

In this article we give unprovability proofs of several combinatorial statements using the method of indiscernibles. Our first two statements are strong versions of KM (the Kanamori-McAloon principle) and KM(2), (the Kanamori-McAloon principle for pairs) that both allow unexpectedly simple proofs. We proceed to discuss results by A.Weiermann and G.Lee on IΣkprovability/unprovability of the prin...