Set Theory and Logic


A Difficulty in Proof Theory

Authors: Thomas Colignatus

Adding some reasonable properties to the Gödelian system of Peano Arithmetic creates a new system for which Gödel's completeness theorems collapse and the Gödeliar becomes the Liar paradox again. Rejection of those properties is difficult since they are reasonable. Three-valued logic is a better option to deal with the Liar and its variants.

Comments: 10 Pages. Paper of 2007, written in Mathematica

Download: PDF

Submission history

[v1] 2014-12-25 05:58:23

Unique-IP document downloads: 68 times

Articles available on are pre-prints that may not yet have been verified by peer-review and should therefore be treated as preliminary and speculative. Nothing stated should be treated as sound unless confirmed and endorsed by a concensus of independent qualified experts. In particular anything that appears to include financial or legal information or proposed medical treatments should not be taken as such. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus