國立高雄大學圖資館 |

Language: English

Back

Foundations of finitely supported st...

Alexandru, Andrei.

Foundations of finitely supported structuresa set theoretical viewpoint /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Foundations of finitely supported structuresby Andrei Alexandru, Gabriel Ciobanu.
Reminder of title:	a set theoretical viewpoint /
Author:	Alexandru, Andrei.
other author:	Ciobanu, Gabriel.
Published:	Cham :Springer International Publishing :2020.
Description:	xi, 204 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Set theory.
Online resource:	https://doi.org/10.1007/978-3-030-52962-8
ISBN:	9783030529628$q(electronic bk.)

Foundations of finitely supported structuresa set theoretical viewpoint /
Alexandru, Andrei.

Foundations of finitely supported structuresa set theoretical viewpoint /[electronic resource] :by Andrei Alexandru, Gabriel Ciobanu. - Cham :Springer International Publishing :2020. - xi, 204 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9783030529628$q(electronic bk.)

Standard No.: 10.1007/978-3-030-52962-8doiSubjects--Topical Terms:

190892
Set theory.

LC Class. No.: QA248

Dewey Class. No.: 511.322

Foundations of finitely supported structuresa set theoretical viewpoint /
LDR:03386nmm a2200337 a 4500 001 583459
003 DE-He213
005 20200720111720.0
006 m d
007 cr nn 008maaau
008 210202s2020 sz s 0 eng d
020 $a 9783030529628$q(electronic bk.)
020 $a 9783030529611$q(paper)
024 7 $a 10.1007/978-3-030-52962-8 $2 doi
035 $a 978-3-030-52962-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA248
072 7 $a UY $2 bicssc
072 7 $a COM014000 $2 bisacsh
072 7 $a UY $2 thema
072 7 $a UYA $2 thema
082 0 4 $a 511.322 $2 23
090 $a QA248 $b .A383 2020
100 1 $a Alexandru, Andrei. $3 753194
245 1 0 $a Foundations of finitely supported structures $h [electronic resource] : $b a set theoretical viewpoint / $c by Andrei Alexandru, Gabriel Ciobanu.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xi, 204 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
520 $a 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.
650 0 $a Set theory. $3 190892
650 0 $a Finite element method. $3 184533
650 1 4 $a Theory of Computation. $3 274475
650 2 4 $a Mathematics of Computing. $3 273710
650 2 4 $a Mathematical Logic and Foundations. $3 274479
700 1 $a Ciobanu, Gabriel. $3 250690
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-030-52962-8
950 $a Computer Science (SpringerNature-11645)