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Logic Journal of IGPL Advance Access originally published online on November 9, 2008
Logic Journal of IGPL 2008 16(6):585-590; doi:10.1093/jigpal/jzn023
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Vol. 16 No. 6, © The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The Ricean Objection: An Analogue of Rice's Theorem for First-order Theories

Igor Carboni Oliveira and Walter Carnielli

Centre for Logic, Epistemology and the History of Science (CLE), and Department of Philosophy (IFCH), State University of Campinas - UNICAMP, C.P. 6133 - 13083-970 Campinas, SP, Brazil.

We propose here an extension of Rice's Theorem to first-order logic, proven by totally elementary means. If P is any property defined over the collection of all first-order theories and P is non-trivial over the set of finitely axiomatizable theories (i.e., P holds for some, but not all theories), then P is undecidable. This not only means that the problem of deciding properties of first-order theories is as hard as the problem of deciding properties about languages accepted by Turing machines, but also offers a general setting for proving several undecidability results in first-order theories.



References

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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow An erratum has been published
Right arrow An erratum has been published
Right arrow Alert me when this article is cited
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