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Characterization classes defined without equality

R. Elgueta

Studia Logica 58 (3):357-394 (1997)

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Categorical abstract algebraic logic: The Diagram and the Reduction Operator Lemmas.George Voutsadakis - 2007 - Mathematical Logic Quarterly 53 (2):147-161.details The study of structure systems, an abstraction of the concept of first-order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first-order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality-free first-order structures are provided in the framework of structure systems. (© 2007 WILEY-VCH (...) Download Export citation Bookmark
First order logic without equality on relativized semantics.Amitayu Banerjee & Mohamed Khaled - 2018 - Annals of Pure and Applied Logic 169 (11):1227-1242.details Download Export citation Bookmark 2 citations
On the Closure Properties of the Class of Full G-models of a Deductive System.Josep Maria Font, Ramon Jansana & Don Pigozzi - 2006 - Studia Logica 83 (1-3):215-278.details In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures (...) Download Export citation Bookmark 9 citations
Lattices of Theories in Languages without Equality.J. B. Nation - 2013 - Notre Dame Journal of Formal Logic 54 (2):167-175.details If $\mathbf{S}$ is a semilattice with operators, then there is an implicational theory $\mathscr{Q}$ such that the congruence lattice $\operatorname{Con}$ is isomorphic to the lattice of all implicational theories containing $\mathscr{Q}$. Download Export citation Bookmark
Algebraic Characterizations for Universal Fragments of Logic.Raimon Elgueta - 1999 - Mathematical Logic Quarterly 45 (3):385-398.details In this paper we address our efforts to extend the well-known connection in equational logic between equational theories and fully invariant congruences to other–possibly infinitary–logics. In the special case of algebras, this problem has been formerly treated by H. J. Hoehnke [10] and R. W. Quackenbush [14]. Here we show that the connection extends at least up to the universal fragment of logic. Namely, we establish that the concept of universal theory matches the abstract notion of fully invariant system. We (...) Download Export citation Bookmark 1 citation
Freeness in classes without equality.Raimon Elgueta - 1999 - Journal of Symbolic Logic 64 (3):1159-1194.details This paper is a continuation of [27], where we provide the background and the basic tools for studying the structural properties of classes of models over languages without equality. In the context of such languages, it is natural to make distinction between two kinds of classes, the so-called abstract classes, which correspond to those closed under isomorphic copies in the presence of equality, and the reduced classes, i.e., those obtained by factoring structures by their largest congruences. The generic problem described (...) Download Export citation Bookmark 1 citation

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