An addendum to "The theory of implicit operations"

Luca Carai; Miriam Kurtzhals; Tommaso Moraschini

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arXiv · 2601.00006

An addendum to "The theory of implicit operations"

Luca Carai·Miriam Kurtzhals·Tommaso Moraschini

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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 congruence preserving Beth companion, but no simple Beth companion.

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Luca Carai, Miriam Kurtzhals, Tommaso Moraschini. 2025-12-16. An addendum to "The theory of implicit operations". https://arxiv.org/abs/2601.00006

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