Set Theory and Logic


Shortest Refutation of Gödel's Completeness Theorem Copyright © 2018 by Colin James III All Rights Reserved.

Authors: Colin James III

"By Gödel's completeness result, the formula (∀x.R(x,x))→(∀x∃y.R(x,y)) holds in all structures, and hence must have a natural deduction proof." We prove the formula is not tautologous, meaning it does not hold in all structures and serves as a contra-example. Hence Gödel's completeness theorem is refuted.

Comments: 1 Page. Copyright © 2018 by Colin James III All rights reserved. Note that comments on Disqus are not forwarded or read, so respond to author's email address: info@cec-services dot com.

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[v1] 2018-07-09 06:47:49

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