Implicit definition of the quaternary discriminator

Campercholi, Miguel; Vaggione, Diego

doi:10.1007/s00012-012-0189-9

Cited by 15 publications

(17 citation statements)

References 10 publications

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“…The next result discloses the semantic meaning of inconsistency terms. It should be observed that algebraic versions of it first appeared in [41] and [16] in the setting of varieties and quasi-varieties of algebras respectively. Lemma 36.…”

Section: Remark 35mentioning

confidence: 99%

Logics of left variable inclusion and Płonka sums of matrices

2020

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The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic . We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic is related to the construction of Płonka sums of the matrix models of . This observation allows to obtain a Hilbert-style axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, and to locate them in the Leibniz hierarchy.

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Section: Remark 35mentioning

confidence: 99%

Logics of left variable inclusion and Płonka sums of matrices

2020

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“…From (5) we obtain a − 1 / ∈r. If a ′ = 0 or a ′ − 1 ∈r a reasoning analogous to the one used in the sub case a ′ ∈r above shows that a ′ + 1 θ a − 1, and so we can take b ′ = a ′ + 1.…”

Section: Congruences Of a Linementioning

confidence: 99%

“…Algebraic functions are a natural generalization of term-functions; they share many of the basic properties of term-functions and every term-function is an algebraic function [3]. An interesting example of a result linking equationally definable functions to structural properties can be found in [5].…”

Section: Introductionmentioning

confidence: 99%

The lattice of congruences of a finite line frame

Areces

Campercholi

Penazzi

et al. 2017

Journal of Logic and Computation

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Let F = F, R be a finite Kripke frame. A congruence of F is a bisimulation of F that is also an equivalence relation on F. The set of all congruences of F is a lattice under the inclusion ordering. In this article we investigate this lattice in the case that F is a finite line frame. We give concrete descriptions of the join and meet of two congruences with a nontrivial upper bound. Through these descriptions we show that for every nontrivial congruence ρ, the interval [Id F , ρ] embeds into the lattice of divisors of a suitable positive integer. We also prove that any two congruences with a nontrivial upper bound permute.

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“…As shown in [6], it is possible to describe those algebras in which the quaternary discriminator is monoalgebraic, i.e., algebraic and definable by an EFD-sentence with only one existential quantifier. Theorem 3.4 ([6]) Let A be a finite algebra and let Q be the quasivariety generated by A.…”

Section: Corollary 33 Suppose a Is A Finite Algebra Having The Discrmentioning

confidence: 99%

Algebraic functions in quasiprimal algebras

Campercholi

Vaggione

2014

Mathematical Logic Qtrly

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A function is algebraic on an algebra A if it can be implicitly defined by a system of equations on A. In this note we give a semantic characterization for algebraic functions on quasiprimal algebras. This characterization is applied to obtain necessary and sufficient conditions for a quasiprimal algebra A to have every one of its algebraic functions be a term function. We also apply our results to particular algebras such as finite fields and monadic algebras.

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Implicit definition of the quaternary discriminator

Cited by 15 publications

References 10 publications

Logics of left variable inclusion and Płonka sums of matrices

Logics of left variable inclusion and Płonka sums of matrices

The lattice of congruences of a finite line frame

Algebraic functions in quasiprimal algebras

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