Abstract
We shall prove in this chapter that in a strong theory Г, some statements which naturally assert the consistency of Г cannot be proved within Г. This famous result of Gödel shows that our ordinary first-order languages have a severe limitation as far as any project for a thorough-going check on the consistency of mathematics is concerned. Historically, the theorem caused a major change of emphasis in foundational research away from a preoccupation with consistency proofs.
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Bibliography
Feferman, S. Arithmetization of metamathematics in a general setting. Fund. Math., 49 (1960), 35–92.
Löb, M. H. Solution of a problem of Leon Henkin, J. Symb. Logic, 20 (1955), 115–118.
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© 1976 Springer-Verlag Inc.
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Monk, J.D. (1976). Unprovability of Consistency. In: Mathematical Logic. Graduate Texts in Mathematics, vol 37. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9452-5_18
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DOI: https://doi.org/10.1007/978-1-4684-9452-5_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9454-9
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