Set Theory and Logic


Refutation of Second Incompleteness Theorem and Well-Foundedness of Jump Hierarchies

Authors: Colin James III

We evaluate Gödel’s second incompleteness theorem (equated to well-founded Kripke-frames and the least element principle) and modal Löb’s theorem (equated to induction). Both are not tautologous and converse. Hence to imply well-foundedness, such as to jump hierarchies, is also not tautologous. These conjectures form a non tautologous fragment of the universal logic VŁ4.

Comments: 2 Pages. Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at

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[v1] 2019-09-25 06:36:10

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