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The theory of Boolean algebras with a distinguished subalgebra is undecidable. (English) Zbl 0354.02036


MSC:

03B25 Decidability of theories and sets of sentences
03G05 Logical aspects of Boolean algebras
03G15 Cylindric and polyadic algebras; relation algebras
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References:

[1] Yu. L. Ershov , Decidability of relatively complemented distributive lattices and the theory of filters , Algebra i. Logika Sem. 3 ( 1964 ), p. 5 - 12 . · Zbl 0199.03103
[2] L. Henkin and J.D. Monk , Cylindric algebras and related structures , Proceedings of the Tarski Symposium, 1974 , p. 105 - 121 . MR 376346 | Zbl 0307.02041 · Zbl 0307.02041
[3] L. Henkin , J.D. Monk and A. Tarski , Cylindric Algebras , North-Holland , 1971 . MR 314620 | Zbl 0576.03043 · Zbl 0576.03043
[4] M.O. Rabin , Decidability of second order theories and automata on infinite trees , Trans. Amer. Math. Soc. 141 ( 1969 ) 1 - 35 . MR 246760 | Zbl 0221.02031 · Zbl 0221.02031 · doi:10.2307/1995086
[5] A. Tarski , Arithmetical classes and types of Boolean algebras , Bull. Amer. Math. Soc. 55 ( 1949 ), p. 64 . · Zbl 0041.34502
[6] C.C. Chang and H.J. Keisler , Model theory , North-Holland , 1973 . Zbl 0276.02032 · Zbl 0276.02032
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