Foundations of finitely supported structures : a set theoretical viewpoint
 Responsibility
 Andrei Alexandru, Gabriel Ciobanu.
 Imprint
 Cham : Springer, 2020.
 Physical description
 1 online resource (205 pages)
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Description
Creators/Contributors
 Author/Creator
 Alexandru, Andrei.
 Contributor
 Ciobanu, Gabriel.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 The World of Structures with Finite Supports. Finitely Supported Sets: Formal Results. Choice Principles in Finitely Supported Mathematics. Connections with Tarski's Concept of Logicality. Partially Ordered Sets in Finitely Supported Mathematics. Lattices in Finitely Supported Mathematics. Constructions of Lattices in Finitely Supported Mathematics. Galois Connections in Finitely Supported Mathematics. Several Forms of Infinity in Finitely Supported Mathematics. Properties of Atoms in Finitely Supported Mathematics. Freshness in Finitely Supported Mathematics. Abstraction in Finitely Supported Mathematics. Relaxing the Finite Support Requirement.
 (source: Nielsen Book Data)
 Publisher's summary

This book presents a set theoretical development for the foundations of the theory of atomic and finitely supported structures. It analyzes whether a classical result can be adequately reformulated by replacing a 'nonatomic structure' with an 'atomic, finitely supported structure'. It also presents many specific properties, such as finiteness, cardinality, connectivity, fixed point, order and uniformity, of finitely supported atomic structures that do not have nonatomic correspondents. In the framework of finitely supported sets, the authors analyze the consistency of various forms of choice and related results. They introduce and study the notion of 'cardinality' by presenting various order and arithmetic properties. Finitely supported partially ordered sets, chain complete sets, lattices and Galois connections are studied, and new fixed point, calculability and approximation properties are presented. In this framework, the authors study the finitely supported Lfuzzy subsets of a finitely supported set and the finitely supported fuzzy subgroups of a finitely supported group. Several pairwise nonequivalent definitions for the notion of 'infinity' (Dedekind infinity, Mostowski infinity, Kuratowski infinity, Tarski infinity, ascending infinity) are introduced, compared and studied in the new framework. Relevant examples of sets that satisfy some forms of infinity while not satisfying others are provided. Uniformly supported sets are analyzed, and certain surprising properties are presented. Finally, some variations of the finite support requirement are discussed. The book will be of value to researchers in the foundations of set theory, algebra and logic.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2020
 ISBN
 9783030529628 (electronic bk.)
 3030529622 (electronic bk.)
 3030529614
 9783030529611