Foundations Of Finitely Supported Structures
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Foundations of Finitely Supported Structures
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. The book will be of value to researchers in the foundations of set theory, algebra and logic.
Foundations of Software Science and Computational Structures
Author: Helmut Seidl
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-07-02
This book constitutes the refereed proceedings of the 10th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2007, held in Braga, Portugal in March/April 2007. The 25 revised full papers presented together with the abstract of one invited talk cover a broad spectrum on theories and methods to support analysis, synthesis, transformation and verification of programs and software systems.
Foundations of Software Science and Computational Structures
This book contains the proceedings of the 11th International Conference on Foundations of Software Science and Computational Structures. It covers theories and methods to support analysis, synthesis, transformation and verification of software systems.