國立虎尾科技大學 |

Foundations of Finitely Supported Structures = A Set Theoretical Viewpoint /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Foundations of Finitely Supported Structures/ by Andrei Alexandru, Gabriel Ciobanu.
Reminder of title:	A Set Theoretical Viewpoint /
Author:	Alexandru, Andrei.
other author:	Ciobanu, Gabriel.
Description:	XI, 204 p. 2 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Computers. -
Online resource:	https://doi.org/10.1007/978-3-030-52962-8
ISBN:	9783030529628

Foundations of Finitely Supported Structures = A Set Theoretical Viewpoint /
Alexandru, Andrei.

Foundations of Finitely Supported StructuresA Set Theoretical Viewpoint /[electronic resource] :by Andrei Alexandru, Gabriel Ciobanu. - 1st ed. 2020. - XI, 204 p. 2 illus.online resource.

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

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

565115
Computers.

LC Class. No.: QA75.5-76.95

Dewey Class. No.: 004.0151

Foundations of Finitely Supported Structures = A Set Theoretical Viewpoint /
LDR:03781nam a22004215i 4500 001 1027407
003 DE-He213
005 20200720111720.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030529628 $9 978-3-030-52962-8
024 7 $a 10.1007/978-3-030-52962-8 $2 doi
035 $a 978-3-030-52962-8
050 4 $a QA75.5-76.95
050 4 $a QA76.63
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 004.0151 $2 23
100 1 $a Alexandru, Andrei. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1111272
245 1 0 $a Foundations of Finitely Supported Structures $h [electronic resource] : $b A Set Theoretical Viewpoint / $c by Andrei Alexandru, Gabriel Ciobanu.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a XI, 204 p. 2 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Computers. $3 565115
650 0 $a Computer science—Mathematics. $3 1253519
650 0 $a Mathematical logic. $2 bicssc $3 810627
650 1 4 $a Theory of Computation. $3 669322
650 2 4 $a Mathematics of Computing. $3 669457
650 2 4 $a Mathematical Logic and Foundations. $3 669393
700 1 $a Ciobanu, Gabriel. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 815308
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030529611
776 0 8 $i Printed edition: $z 9783030529635
776 0 8 $i Printed edition: $z 9783030529642
856 4 0 $u https://doi.org/10.1007/978-3-030-52962-8
912 $a ZDB-2-SCS
912 $a ZDB-2-SXCS
950 $a Computer Science (SpringerNature-11645)
950 $a Computer Science (R0) (SpringerNature-43710)