An addendum to "The theory of implicit operations"
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
TL;DR
This paper presents counterexamples related to the theory of implicit operations, including a pp expansion that is not a variety and a sequence of varieties with a special congruence property.
Contribution
It introduces specific counterexamples and constructions that challenge existing assumptions in the theory of implicit operations.
Findings
A pp expansion of a variety that is not a variety.
A sequence of varieties with a nonequational congruence preserving Beth companion.
Abstract
In this addendum to [4], we provide a pair of counterexamples relevant to the theory of implicit operations. More precisely, we exhibit a pp expansion of a variety that fails to be a variety (although it is a quasivariety). Furthermore, we construct a sequence of varieties possessing a nonequational congruence preserving Beth companion.
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Taxonomy
TopicsAdvanced Algebra and Logic · Fuzzy and Soft Set Theory · Rings, Modules, and Algebras