Geodesic
Generalized deductive systems in subregular varieties
Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 319-324

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MR Zbl
An algebra ${\mathcal A}= (A,F)$ is subregular alias regular with respect to a unary term function $g$ if for each $\Theta , \Phi \in \text{Con}\,{\mathcal A}$ we have $\Theta = \Phi $ whenever $[g(a)]_{\Theta } = [g(a)]_{\Phi }$ for each $a\in A$. We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset $C\subseteq A$ is a class of some congruence on $\Theta $ containing $g(a)$ if and only if $C$ is this generalized deductive system. This method is efficient (needs a finite number of steps).
An algebra ${\mathcal A}= (A,F)$ is subregular alias regular with respect to a unary term function $g$ if for each $\Theta , \Phi \in \text{Con}\,{\mathcal A}$ we have $\Theta = \Phi $ whenever $[g(a)]_{\Theta } = [g(a)]_{\Phi }$ for each $a\in A$. We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset $C\subseteq A$ is a class of some congruence on $\Theta $ containing $g(a)$ if and only if $C$ is this generalized deductive system. This method is efficient (needs a finite number of steps).
DOI : 10.21136/MB.2003.134184
Classification : 03B22, 08A30, 08B05
Keywords: regular variety; subregular variety; deductive system; congruence class; difference system 
Chajda, Ivan. Generalized deductive systems in subregular varieties. Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 319-324. doi: 10.21136/MB.2003.134184
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