Incompleteness
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[(Up)](../../README.md#topics) | _See also: [FoM](../FoM/README.md#fom), [Logic](../Logic/README.md#logic)_

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### Web resources

[What axioms are used to prove Gödel's Incompleteness Theorems?](https://mathoverflow.net/questions/118183/what-axioms-are-used-to-prove-g%C3%B6dels-incompleteness-theorems) ★

[Finite versions of Godel\' s incompleteness](http://mathoverflow.net/questions/100898/finite-versions-of-godel-s-incompleteness) ★

[Can this provide an example of incompleteness under the assumption of mere consistency?](https://mathoverflow.net/questions/451242/can-this-provide-an-example-of-incompleteness-under-the-assumption-of-mere-consi) ★

[GOEDEL MACHINE SUMMARY](https://people.idsia.ch/~juergen/gmsummary.html) ★

[Burali-Forti paradox - Wikipedia, the free encyclopedia](https://en.wikipedia.org/wiki/Burali-Forti_paradox)

_(in [FoM](../FoM/README.md#fom))_ [Are there first-order statements that second order PA proves that first order PA does not?](https://mathoverflow.net/questions/366580/are-there-first-order-statements-that-second-order-pa-proves-that-first-order-pa) ★

_(in [Theorem Proving](../Theorem%20Proving/README.md#theorem-proving))_ [Do theorems provers demonstrate their own correctness?](https://cs.stackexchange.com/questions/119817/do-theorems-provers-demonstrate-their-own-correctness) ★★★


### Papers

A Simple Character String Proof of the \"True but Unprovable\" Version of Goedel\'s First Incompleteness Theorem (online @ [arxiv.org](https://arxiv.org/abs/1402.7253))

A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points (online @ [arxiv.org](https://arxiv.org/abs/math/0305282))

Self-Verifying Axiom Systems, the Incompleteness Theorem and Related Reflection Principles (online @ [jstor](https://www.jstor.org/stable/2695030))

_(in [Recreational Mathematics](../Recreational%20Mathematics/README.md#recreational-mathematics))_ [Fusible numbers and Peano Arithmetic](https://arxiv.org/abs/2003.14342) ★