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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Lindenbaum algebras and partial conservativity


Author: Christian Bennet
Journal: Proc. Amer. Math. Soc. 97 (1986), 323-327
MSC: Primary 03F25; Secondary 03F30
DOI: https://doi.org/10.1090/S0002-9939-1986-0835891-6
MathSciNet review: 835891
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Abstract: A partial Lindenbaum algebra $ {\Gamma ^A}$, where $ A$ is a theory extending Peano arithmetic and $ \Gamma \in \{ {\Pi _n},{\Sigma _n}\} $, is the full Lindenbaum algebra for $ A$ restricted to sentences in $ A$ provably equivalent to $ {\Gamma _n}$-sentences. Using a new result on pairs of partially conservative sentences, we show that $ \Pi _n^A$ and $ \Sigma _n^A$ are not isomorphic.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0835891-6
Article copyright: © Copyright 1986 American Mathematical Society