On the length of proofs of finitistic consistency statements in first order theories
sciencedirect.com
Gödel's incompleteness theorems meet proof complexity: why the shortest path to certainty in formal mathematics may be provably, impossibly long.
Gödel's Incompleteness TheoremsProof Complexity TheoryHilbert's Finitist ProgramComputational Complexity
Theory Briefing
- Gödel's Second Incompleteness Theorem bars any system from proving its own consistency — this paper probes what happens when you restrict that question to finitistic statements.
- The length of proofs in first-order theories is shown to balloon under consistency demands, exposing a hard complexity ceiling baked into logic itself.
- These findings connect Hilbert's finitist program to modern proof complexity, revealing why some truths are reachable in principle but unreachable in practice.