Lindenbaum algebras and partial conservativity
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- by Christian Bennet
- Proc. Amer. Math. Soc. 97 (1986), 323-327
- DOI: https://doi.org/10.1090/S0002-9939-1986-0835891-6
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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.References
- Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
- S. Feferman, Arithmetization of metamathematics in a general setting, Fund. Math. 49 (1960/61), 35–92. MR 147397, DOI 10.4064/fm-49-1-35-92
- D. Guaspari, Partially conservative extensions of arithmetic, Trans. Amer. Math. Soc. 254 (1979), 47–68. MR 539907, DOI 10.1090/S0002-9947-1979-0539907-7
- Per Lindström, On partially conservative sentences and interpretability, Proc. Amer. Math. Soc. 91 (1984), no. 3, 436–443. MR 744645, DOI 10.1090/S0002-9939-1984-0744645-9
- Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto-London, 1967. MR 0224462
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- 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