CATEGORICAL ABSTRACT ALGEBRAIC LOGIC: OPERATORS ON CLASSES OF STRUCTURE SYSTEMS

• Voutsadakis George

  Lake Superior State University

Abstract

The study of structure systems, an abstraction of the concept of firstorder 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. A variety of operators on classes of structure systems are introduced and studied, taking after similar work of Elgueta in the context of the model theory of equality-free first-order logic. Both Elgueta’s and the present work are inspired by considerations arising in the study of the process of algebraization in abstract algebraic logic. The ways that these various class operators interact, when composed with one-another, are at the focus of current investigations.

Journal

• Scientiae Mathematicae Japonicae

  Scientiae Mathematicae Japonicae 65 (1), 11-25, 2007

  International Society for Mathematical Sciences

Keywords

• Structure Systems
• Congruence Systems
• Leibniz Congruence Systems
• Strong System Morphisms
• Products
• Reduced Products
• Subdirect Products
• Leibniz-Reduced Structures
• Reductions
• Expansions
• Filter Extensions

Details

• CRID: 1390002184880236672
• NII Article ID: 10018893752
• NII Book ID: AA1150654X
• DOI: 10.32219/isms.65.1_11
• ISSN: 13460447
• Text Lang: en
• Data Source:
  • JaLC
  • CiNii Articles
• Abstract License Flag: Disallowed