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Journal of Logic and Computation Advance Access published online on August 12, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp048
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Can we make the Second Incompleteness Theorem Coordinate Free?

Albert Visser

Department of Philosophy, Utrecht University, Heidelberglaan 8, 3584 CS Utrecht, The Netherlands.
E-mail: albert.visser{at}phil.uu.nl

Received 9 August 2008.


  Abstract

Is it possible to give a coordinate-free formulation of the Second Incompleteness Theorem? We pursue one possible approach to this question. We show that (i) cutfree consistency for finitely axiomatized theories can be uniquely characterized modulo EA-provable equivalence and (ii) consistency for finitely axiomatized sequential theories can be uniquely characterized modulo EA-provable equivalence. The case of infinitely axiomatized RE theories is more delicate. We carefully discuss this in the article.

Keywords: Second Incompleteness Theorem; interpretability


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