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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On partially conservative sentences and interpretability


Author: Per Lindström
Journal: Proc. Amer. Math. Soc. 91 (1984), 436-443
MSC: Primary 03F25; Secondary 03F30
MathSciNet review: 744645
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Abstract: A sentence $ \varphi $ is $ \Gamma $-conservative over $ T$ if $ T + \varphi \vdash \psi $ implies $ T \vdash \psi $ for every $ \psi \in \Gamma $. In §1 this concept for $ \Gamma = \sum _{n + 1}^0$ and $ \prod _{n + 1}^0$ is investigated. In §2 results from §1 are applied to interpretability in theories containing arithmetic.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0744645-9
PII: S 0002-9939(1984)0744645-9
Article copyright: © Copyright 1984 American Mathematical Society