東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Finitely supported mathematics = an ...

Alexandru, Andrei.

Linked to FindBook

Google Book

Amazon

博客來

Finitely supported mathematics = an introduction /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Finitely supported mathematics/ by Andrei Alexandru, Gabriel Ciobanu.
Reminder of title:	an introduction /
Author:	Alexandru, Andrei.
other author:	Ciobanu, Gabriel.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	vii, 185 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Fraenkel-Mostowski Set Theory: A Framework for Finitely Supported Mathematics -- Algebraic Structures in Finitely Supported Mathematics -- Extended Fraenkel-Mostowski Set Theory -- Process Calculi in Finitely Supported Mathematics -- References.
Contained By:	Springer eBooks
Subject:	Mathematics. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-42282-4
ISBN:	9783319422824

Finitely supported mathematics = an introduction /
Alexandru, Andrei.

Finitely supported mathematicsan introduction /[electronic resource] :by Andrei Alexandru, Gabriel Ciobanu. - Cham :Springer International Publishing :2016. - vii, 185 p. :ill., digital ;24 cm.

Introduction -- Fraenkel-Mostowski Set Theory: A Framework for Finitely Supported Mathematics -- Algebraic Structures in Finitely Supported Mathematics -- Extended Fraenkel-Mostowski Set Theory -- Process Calculi in Finitely Supported Mathematics -- References.

In this book the authors present an alternative set theory dealing with a more relaxed notion of infiniteness, called finitely supported mathematics (FSM) It has strong connections to the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel (ZF) set theory with atoms and to the theory of (generalized) nominal sets. More exactly, FSM is ZF mathematics rephrased in terms of finitely supported structures, where the set of atoms is infinite (not necessarily countable as for nominal sets) In FSM, 'sets' are replaced either by `invariant sets' (sets endowed with some group actions satisfying a finite support requirement) or by `finitely supported sets' (finitely supported elements in the powerset of an invariant set) It is a theory of `invariant algebraic structures' in which infinite algebraic structures are characterized by using their finite supports. After explaining the motivation for using invariant sets in the experimental sciences as well as the connections with the nominal approach, admissible sets and Gandy machines (Chapter 1), the authors present in Chapter 2 the basics of invariant sets and show that the principles of constructing FSM have historical roots both in the definition of Tarski `logical notions' and in the Erlangen Program of Klein for the classification of various geometries according to invariants under suitable groups of transformations. Furthermore, the consistency of various choice principles is analyzed in FSM. Chapter 3 examines whether it is possible to obtain valid results by replacing the notion of infinite sets with the notion of invariant sets in the classical ZF results. The authors present techniques for reformulating ZF properties of algebraic structures in FSM. In Chapter 4 they generalize FM set theory by providing a new set of axioms inspired by the theory of amorphous sets, and so defining the extended Fraenkel-Mostowski (EFM) set theory. In Chapter 5 they define FSM semantics for certain process calculi (e.g., fusion calculus), and emphasize the links to the nominal techniques used in computer science. They demonstrate a complete equivalence between the new FSM semantics (defined by using binding operators instead of side conditions for presenting the transition rules) and the known semantics of these process calculi. The book is useful for researchers and graduate students in computer science and mathematics, particularly those engaged with logic and set theory.

ISBN: 9783319422824

Standard No.: 10.1007/978-3-319-42282-4doiSubjects--Topical Terms:

515831
Mathematics.

LC Class. No.: QA248 / .A44 2016

Dewey Class. No.: 511.322

Finitely supported mathematics = an introduction /
LDR:03722nmm a2200337 a 4500 001 2043400
003 DE-He213
005 20161215144806.0
006 m d
007 cr nn 008maaau
008 170217s2016 gw s 0 eng d
020 $a 9783319422824 $q (electronic bk.)
020 $a 9783319422817 $q (paper)
024 7 $a 10.1007/978-3-319-42282-4 $2 doi
035 $a 978-3-319-42282-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA248 $b .A44 2016
072 7 $a UY $2 bicssc
072 7 $a UYA $2 bicssc
072 7 $a COM014000 $2 bisacsh
072 7 $a COM031000 $2 bisacsh
082 0 4 $a 511.322 $2 23
090 $a QA248 $b .A383 2016
100 1 $a Alexandru, Andrei. $3 2203179
245 1 0 $a Finitely supported mathematics $h [electronic resource] : $b an introduction / $c by Andrei Alexandru, Gabriel Ciobanu.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a vii, 185 p. : $b ill., digital ; $c 24 cm.
505 0 $a Introduction -- Fraenkel-Mostowski Set Theory: A Framework for Finitely Supported Mathematics -- Algebraic Structures in Finitely Supported Mathematics -- Extended Fraenkel-Mostowski Set Theory -- Process Calculi in Finitely Supported Mathematics -- References.
520 $a In this book the authors present an alternative set theory dealing with a more relaxed notion of infiniteness, called finitely supported mathematics (FSM) It has strong connections to the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel (ZF) set theory with atoms and to the theory of (generalized) nominal sets. More exactly, FSM is ZF mathematics rephrased in terms of finitely supported structures, where the set of atoms is infinite (not necessarily countable as for nominal sets) In FSM, 'sets' are replaced either by `invariant sets' (sets endowed with some group actions satisfying a finite support requirement) or by `finitely supported sets' (finitely supported elements in the powerset of an invariant set) It is a theory of `invariant algebraic structures' in which infinite algebraic structures are characterized by using their finite supports. After explaining the motivation for using invariant sets in the experimental sciences as well as the connections with the nominal approach, admissible sets and Gandy machines (Chapter 1), the authors present in Chapter 2 the basics of invariant sets and show that the principles of constructing FSM have historical roots both in the definition of Tarski `logical notions' and in the Erlangen Program of Klein for the classification of various geometries according to invariants under suitable groups of transformations. Furthermore, the consistency of various choice principles is analyzed in FSM. Chapter 3 examines whether it is possible to obtain valid results by replacing the notion of infinite sets with the notion of invariant sets in the classical ZF results. The authors present techniques for reformulating ZF properties of algebraic structures in FSM. In Chapter 4 they generalize FM set theory by providing a new set of axioms inspired by the theory of amorphous sets, and so defining the extended Fraenkel-Mostowski (EFM) set theory. In Chapter 5 they define FSM semantics for certain process calculi (e.g., fusion calculus), and emphasize the links to the nominal techniques used in computer science. They demonstrate a complete equivalence between the new FSM semantics (defined by using binding operators instead of side conditions for presenting the transition rules) and the known semantics of these process calculi. The book is useful for researchers and graduate students in computer science and mathematics, particularly those engaged with logic and set theory.
650 0 $a Mathematics. $3 515831
650 0 $a Set theory. $3 520081
650 1 4 $a Computer Science. $3 626642
650 2 4 $a Theory of Computation. $3 892514
650 2 4 $a Mathematics of Computing. $3 891213
650 2 4 $a Mathematical Logic and Foundations. $3 892656
650 2 4 $a Algebra. $3 516203
700 1 $a Ciobanu, Gabriel. $3 1070810
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-42282-4
950 $a Computer Science (Springer-11645)