Abstract
We note that a class of models is subdirect product closed if and only if it is definable by a class of L ∞∞-sentences of a special form.
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Baldwin, J.T., Samhan, M.A.: On the definability of PS(A). Algebra Universalis 23(3), 254–261 (1986). DOI 10.1007/BF01230620. URL http://dx.doi.org/10.1007/BF01230620
Birkhoff G.: Subdirect unions in universal algebra. Bull. Amer. Math. Soc. 50, 764–768 (1944)
Blok, W.J., Pigozzi, D.: Algebraic semantics for universal Horn logic without equality. In: Universal algebra and quasigroup theory (Jadwisin, 1989), Res. Exp. Math., vol. 19, pp. 1–56. Heldermann, Berlin (1992)
Czelakowski, J.: Protoalgebraic logics, Trends in Logic—Studia Logica Library, vol. 10. Kluwer, Dordrecht (2001)
Czelakowski J.: The Suszko operator. Part I. Studia Logica 54(1-2), 181–231 (2003)
Gorbunov, V.A.: Algebraicheskaya Teoriya Kvazimnogoobrazij. Nauchnaya Kniga, Novosibirsk (1999). English transl. Algebraic Theory of Quasivarieties, Consultants Bureau, New York (1998)
Grätzer G.: On the class of subdirect powers of a finite algebra. Acta Sci. Math. (Szeged) 25, 160–168 (1964)
Grätzer, G.: Universal algebra, 2nd edn. Springer, New York (1979)
Lyndon R.C.: Properties preserved in subdirect products. Pacific J. Math. 9, 155–164 (1959)
Lyndon R.C.: Properties preserved under algebraic constructions. Bull. Amer. Math. Soc. 65, 287–299 (1959)
Shafaat A.: On implicationally defined classes of algebras. J. London Math. Soc. 44, 137–140 (1969)
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Presented by J. Adamek.
This work was supported by Polish National Science Centre grant number DEC- 2011/01/D/ST1/06136.
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Stronkowski, M.M. Defining subdirect product closed classes in infinitary logic. Algebra Univers. 69, 231–235 (2013). https://doi.org/10.1007/s00012-013-0230-7
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DOI: https://doi.org/10.1007/s00012-013-0230-7