Abstract
This chapter plays a twofold role in the book. Firstly, the chapter surveys basic facts about quasivarieties of algebras. These facts are widely utilised in the subsequent chapters devoted to algebraizable logics. Secondly, the chapter shows how the methods initially elaborated for protoalgebraic sentential logics in the first part can be also applied in the area of equational logic. Most of the results presented in this chapter are proved by way of adapting the purely consequential methods of sentential logic to the needs of the (quasi) equational systems associated with quasivarieties of algebras.
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Notes for Chapter Q
Czelakowski, J. and Dziobiak, W. [1982] Another proof that ISPT (K] is the least quasivariety containing K, Studia Logica 41, 343–345.
Mal’cev, A.I. [1966] A few remarks on quasivarieties of algebraic systems (in Russian), Algebra i Logika, Seminar 5, 3–9. English translation in Mal’cev [1971].
Grätzer, G. and Lakser, H. [1973] A note on the implicational class generated by a class of structures, Canadian Mathematical Bulletin 16, 603–605.
Czelakowski, J. [1996] Filtered subdirect products, Bulletin of the Section of Logic 24, University of Lodi, 92–96.
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© 2001 Springer Science+Business Media Dordrecht
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Czelakowski, J. (2001). Quasivarieties of Algebras. In: Protoalgebraic Logics. Trends in Logic, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2807-2_6
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DOI: https://doi.org/10.1007/978-94-017-2807-2_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5693-1
Online ISBN: 978-94-017-2807-2
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