In this paper we investigate subtractive varieties of algebras that are Fregean in order to get structure theorems about them. For instance it turns out that a subtractive variety is Fregean and has equationally definable principal congruences if and only if it is termwise equivalent to a variety of Hilbert algebras with compatible operations. Several examples are provided to illustrate the theory.
Agliano', P. (2001). Fregean subtractive varieties with definable congruence. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 71(3), 353-366 [10.1017/S1446788700002998].
Fregean subtractive varieties with definable congruence
Agliano', Paolo
2001-01-01
Abstract
In this paper we investigate subtractive varieties of algebras that are Fregean in order to get structure theorems about them. For instance it turns out that a subtractive variety is Fregean and has equationally definable principal congruences if and only if it is termwise equivalent to a variety of Hilbert algebras with compatible operations. Several examples are provided to illustrate the theory.
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https://hdl.handle.net/11365/1013855