0
Your cart

Your cart is empty

Books > Science & Mathematics > Mathematics > Algebra

Buy Now

Finitely Supported Mathematics - An Introduction (Hardcover, 1st ed. 2016) Loot Price: R1,950
Discovery Miles 19 500
You Save: R1,251 (39%)
Finitely Supported Mathematics - An Introduction (Hardcover, 1st ed. 2016): Andrei Alexandru, Gabriel Ciobanu

Finitely Supported Mathematics - An Introduction (Hardcover, 1st ed. 2016)

Andrei Alexandru, Gabriel Ciobanu

 (sign in to rate)
List price R3,201 Loot Price R1,950 Discovery Miles 19 500 | Repayment Terms: R183 pm x 12* You Save R1,251 (39%)

Bookmark and Share

Expected to ship within 12 - 19 working days

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.

General

Imprint: Springer International Publishing AG
Country of origin: Switzerland
Release date: August 2016
First published: 2016
Authors: Andrei Alexandru • Gabriel Ciobanu
Dimensions: 235 x 155 x 13mm (L x W x T)
Format: Hardcover
Pages: 185
Edition: 1st ed. 2016
ISBN-13: 978-3-319-42281-7
Categories: Books > Computing & IT > General theory of computing > Mathematical theory of computation
Books > Science & Mathematics > Mathematics > Mathematical foundations > Mathematical logic
Books > Science & Mathematics > Mathematics > Mathematical foundations > Set theory
Books > Science & Mathematics > Mathematics > Algebra > General
Promotions
LSN: 3-319-42281-2
Barcode: 9783319422817

Is the information for this product incomplete, wrong or inappropriate? Let us know about it.

Does this product have an incorrect or missing image? Send us a new image.

Is this product missing categories? Add more categories.

Review This Product

No reviews yet - be the first to create one!

You might also like..

A Generalized Framework of Linear…
Liansheng Tan Paperback R2,474 R2,339 Discovery Miles 23 390
Differential Equations with Linear…
Matthew R. Boelkins, Jack L. Goldberg, … Hardcover R3,047 Discovery Miles 30 470
Math of Life and Death
Yates Paperback R460 R427 Discovery Miles 4 270
Linear Algebra and Its Applications…
David Lay, Steven Lay, … Paperback R2,492 Discovery Miles 24 920
Introduction to Analysis - Pearson New…
William Wade Paperback R2,542 Discovery Miles 25 420
Introduction to Linear Algebra
Gilbert Strang Hardcover R2,358 Discovery Miles 23 580
Math Without Numbers
Milo Beckman Paperback R450 R415 Discovery Miles 4 150
The Ten Equations That Rule the World…
David Sumpter Paperback R514 R479 Discovery Miles 4 790
Sets, Groups, and Mappings - An…
Andrew D. Hwang Hardcover R2,424 Discovery Miles 24 240
Deformation Theory of Discontinuous…
Ali Baklouti Hardcover R5,764 Discovery Miles 57 640
Best Books gegradeerde leesreeks: Vlak 1…
Best Books Paperback R95 R90 Discovery Miles 900
Edexcel Award in Algebra Level 3…
Paperback R427 Discovery Miles 4 270

See more

Partners