Is there a consistent, complete axiom system that proves its own consistency?
I know that this question isn't exact and I haven't defined when an axiom system proves its own consistency because that's just human interpretation.
2026-03-27 05:37:37.1774589857
Consistent, complete axiom system that proves its own consistency
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Dan Willard published several papers about this topic in the Journal of Symbolic Logic. One place to start is the short Wikipedia article "Self-verifying theories". I am not familiar with the detailed proofs about Willard's theories, but when I have heard him talk about them he indicated they do not prove that multiplication is a total function, and in that way manage to remain weak enough to avoid the incompleteness theorem.