The theory of boolean algebras with a distinguished subalgebra is undecidable
Annales scientifiques de l'Université de Clermont. Mathématiques, Volume 60 (1976) no. 13, p. 129-134
@article{ASCFM_1976__60_13_129_0,
     author = {Rubin, Matatyahu},
     title = {The theory of boolean algebras with a distinguished subalgebra is undecidable},
     journal = {Annales scientifiques de l'Universit\'e de Clermont. Math\'ematiques},
     publisher = {UER de Sciences exactes et naturelles de l'Universit\'e de Clermont},
     volume = {60},
     number = {13},
     year = {1976},
     pages = {129-134},
     zbl = {0354.02036},
     mrnumber = {465835},
     language = {en},
     url = {http://www.numdam.org/item/ASCFM_1976__60_13_129_0}
}
Rubin, Matatyahu. The theory of boolean algebras with a distinguished subalgebra is undecidable. Annales scientifiques de l'Université de Clermont. Mathématiques, Volume 60 (1976) no. 13, pp. 129-134. http://www.numdam.org/item/ASCFM_1976__60_13_129_0/

[1] Yu. L. Ershov, Decidability of relatively complemented distributive lattices and the theory of filters, Algebra i. Logika Sem. 3 (1964), p. 5-12.

[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

[3] L. Henkin, J.D. Monk and A. Tarski, Cylindric Algebras, North-Holland, 1971. | MR 314620 | 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

[5] A. Tarski, Arithmetical classes and types of Boolean algebras, Bull. Amer. Math. Soc. 55 (1949), p. 64.

[6] C.C. Chang and H.J. Keisler, Model theory, North-Holland, 1973. | Zbl 0276.02032