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001			86271
003			ES-MaUEC
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007			cr nn 008mamaa
008			160726s2016 gw | s |||| 0|eng d
020			_a9783319422824
040			_aES-MaUEC
050		4	_aQA248 _b.A449 2016
082	0	4	_a004.0151
100	1		_aAlexandru, Andrei _0Local _999864
245	1	0	_aFinitely Supported Mathematics : _bAn Introduction _cby Andrei Alexandru, Gabriel Ciobanu
260			_aCham _bSpringer International Publishing _c2016
300			_a1 recurso en línea (VII, 185 páginas) :
336			_aTexto _btxt _2rdacontent
337			_aelectrónico _bc _2rdamedia
338			_arecurso electrónico _bcr _2rdacarrier
505	0		_aIntroduction -- 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	3		_aIn 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.
710	2		_aSpringerLink (Online service) _0Local _9106996
942			_2lcc _cLE
988			_aEBOOK, asignarmaterias , EBSPRINGER
650	0	7	_aOrdenadores _0 _2embne _9138111
650		7	_aMatemáticas _0(OCoLC)1012163 _2embne _0 _9405008
700	1		_aCiobanu, Gabriel _0Local _999865
856	4	0	_uhttps://go.openathens.net/redirector/universidadeuropea.es?url=https://link.springer.com/book/10.1007/978-3-319-42282-4 _zAcceso a este recurso digital (usuarios Universidad Europea de Madrid)
901			_ai9783319422824
907			_a.b12955498 _b10-10-17 _c21-11-16
998			_am _a_alco _a_vill _b - - _cm _dz _e- _feng _ggw _h0
945			_aQA248 .A449 2016 EB _g1 _ieBOOK _j0 _lmae _o- _pEUR0.00 _q- _r- _sb _t15 _u0 _v0 _w0 _x0 _y.i11597604 _z06-04-17
999			_c86271 _d86271 _x1