Geodesic
Algebraic geometry over Boolean algebras in the language with constants
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 197-218.

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We study equations over Boolean algebras with distinguished elements. We prove criteria for when a Boolean algebra is equationally Noetherian, weakly equationally Noetherian, $\mathbf q_\omega$-compact, or $\mathbf u_\omega$-compact. Also we solve the problem of geometric equivalence in the class of Boolean algebras with distinguished elements. 
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A. N. Shevlyakov. Algebraic geometry over Boolean algebras in the language with constants. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 4, pp. 197-218. http://geodesic.mathdoc.fr/item/FPM_2013_18_4_a13/

[1] Daniyarova E. Yu., Myasnikov A. G., Remeslennikov V. N., “Algebraicheskaya geometriya nad algebraicheskimi sistemami. II. Osnovaniya”, Fundament. i prikl. mat., 17:1 (2011/2012), 65–106 | MR

[2] Daniyarova E., Miasnikov A., Remeslennikov V., “Unification theorems in algebraic geometry”, Aspects of Infinite Groups, Algebra Discrete Math., 1, 2008, 80–111 | DOI | MR | Zbl

[3] Daniyarova E., Miasnikov A., Remeslennikov V., “Algebraic geometry over algebraic structures. III. Equationally Noetherian property and compactness”, Southeast Asian Bull. Math., 35 (2011), 35–68 | MR | Zbl

[4] Kotov M., “Equationally Noetherian property and close properties”, Southeast Asian Bull. Math., 35 (2011), 419–429 | MR | Zbl

[5] Monk D., Handbook of Boolean Algebras, Elsevier, 1989

[6] Miasnikov A., Remeslennikov V., “Algebraic geometry over groups. II. Logical foundations”, J. Algebra, 234 (2000), 225–276 | DOI | MR

[7] Plotkin B., “Algebras with the same (algebraic) geometry”, Proc. Steklov Inst. Math., 242, 2003, 165–196 | MR | Zbl

[8] Shevlyakov A., “Algebraic geometry over linear ordered semilattices”, Algebra and Model Theory, 8, eds. A. G. Pinus et al., NSTU, Novosibirsk, 2011, 116–131

[9] Shevlyakov A., “Commutative idempotent semigroups at the service of universal algebraic geometry”, Southeast Asian Bull. Math., 35 (2011), 111–136 | MR | Zbl