caa a22 4500 467882746 CHVBK 20180406152724.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10485-006-9030-y doi (NATIONALLICENCE)springer-10.1007/s10485-006-9030-y Voutsadakis George School of Mathematics and Computer Science, Lake Superior State University, 650 W. Easterday Avenue, 49783, Sault Sainte Marie, MI, USA aut Categorical Abstract Algebraic Logic: Leibniz Equality and Homomorphism Theorems [Elektronische Daten] [George Voutsadakis] The study of structure systems, an abstraction of the concept of first-order structures, is continued. Structure systems have algebraic systems rather than universal algebras as their algebraic reducts. Moreover, their relational component consists of a collection of relation systems on the underlying functors rather than simply a system of relations on a single set. Congruence systems of structure systems are introduced and the Leibniz congruence system of a structure system is defined. Analogs of the Homomorphism, the Second Isomorphism and the Correspondence Theorems of Universal Algebra are provided in this more abstract context. These results generalize corresponding results of Elgueta for equality-free first-order logic. Finally, a version of Gödel's Completeness Theorem is provided with reference to structure systems. Springer Science + Business Media B.V., 2006 structure systems nationallicence congruence systems nationallicence Leibniz congruence systems nationallicence strong system morphisms nationallicence homomorphism theorem nationallicence second isomorphism theorem nationallicence correspondence theorem nationallicence Gödel's completeness theorem nationallicence Applied Categorical Structures Kluwer Academic Publishers 14/4(2006-08-01), 357-376 0927-2852 14:4<357 2006 14 10485 https://doi.org/10.1007/s10485-006-9030-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-006-9030-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Voutsadakis George School of Mathematics and Computer Science, Lake Superior State University, 650 W. Easterday Avenue, 49783, Sault Sainte Marie, MI, USA aut NATIONALLICENCE 773 0- Applied Categorical Structures Kluwer Academic Publishers 14/4(2006-08-01), 357-376 0927-2852 14:4<357 2006 14 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer