Description: Foundations of Finitely Supported Structures : A Set Theoretical Viewpoint, Hardcover by Alexandru, Andrei; Ciobanu, Gabriel, ISBN 3030529614, ISBN-13 9783030529611, Like New Used, Free shipping in the US 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 'non-atomic 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 non-atomic 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 L-fuzzy subsets of a finitely supported set and the finitely supported fuzzy subgroups of a finitely supported group. Several pairwise non-equivalent 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. Th will be of value to researchers in the foundations of set theory, algebra and logic.
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Book Title: Foundations of Finitely Supported Structures : A Set Theoretical
Number of Pages: Xi, 204 Pages
Language: English
Publication Name: Foundations of Finitely Supported Structures : a Set Theoretical ViewPoint
Publisher: Springer International Publishing A&G
Subject: Computer Science, Logic, Applied
Publication Year: 2020
Type: Textbook
Item Weight: 17.4 Oz
Subject Area: Mathematics, Computers
Author: Andrei Alexandru, Gabriel Ciobanu
Item Length: 9.3 in
Item Width: 6.1 in
Format: Hardcover
