0000000000225076

AUTHOR

E. Cosme Llópez

showing 3 related works from this author

When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?

2017

For a set of sorts $S$ and an $S$-sorted signature $\Sigma$ we prove that a profinite $\Sigma$-algebra, i.e., a projective limit of a projective system of finite $\Sigma$-algebras, is a retract of an ultraproduct of finite $\Sigma$-algebras if the family consisting of the finite $\Sigma$-algebras underlying the projective system is with constant support. In addition, we provide a categorial rendering of the above result. Specifically, after obtaining a category where the objects are the pairs formed by a nonempty upward directed preordered set and by an ultrafilter containing the filter of the final sections of it, we show that there exists a functor from the just mentioned category whose o…

Pure mathematicsLogic010102 general mathematicsMathematics::General TopologyMathematics - Category TheoryUltraproduct01 natural sciences03C20 08A68 (Primary) 18A30 (Secondary)010101 applied mathematicsMathematics::Category TheoryFOS: MathematicsCategory Theory (math.CT)Àlgebra0101 mathematicsMathematics
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Congruence-based proofs of the recognizability theorems for free many-sorted algebras

2020

Abstract We generalize several recognizability theorems for free single-sorted algebras to free many-sorted algebras and provide, in a uniform way and without using either regular tree grammars or tree automata, purely algebraic proofs of them based on congruences.

Pure mathematicsLogicComputer science010102 general mathematics0102 computer and information sciencesMathematical proof01 natural sciencesTheoretical Computer ScienceArts and Humanities (miscellaneous)010201 computation theory & mathematicsHardware and ArchitectureCongruence (manifolds)0101 mathematicsComputer Science::Formal Languages and Automata TheorySoftwareJournal of Logic and Computation
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A characterization of the n-ary many-sorted closure operators and a many-sorted Tarski irredundant basis theorem

2018

A theorem of single-sorted algebra states that, for a closure space (A, J ) and a natural number n, the closure operator J on the set A is n-ary if and only if there exists a single-sorted signature Σ and a Σ-algebra A such that every operation of A is of an arity ≤ n and J = SgA, where SgA is the subalgebra generating operator on A determined by A. On the other hand, a theorem of Tarski asserts that if J is an n-ary closure operator on a set A with n ≥ 2, then, for every i, j ∈ IrB(A, J ), where IrB(A, J ) is the set of all natural numbers which have the property of being the cardinality of an irredundant basis (≡ minimal generating set) of A with respect to J , if i < j and {i + 1, . . . …

Existential quantificationClosure (topology)Natural numberCharacterization (mathematics)Space (mathematics)CombinatoricsSet (abstract data type)TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESMathematics (miscellaneous)If and only ifData_FILESClosure operatorMatemàticaMathematicsQuaestiones Mathematicae
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