000 | 04262nam a22005295i 4500 | ||
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001 | 978-3-030-52962-8 | ||
003 | DE-He213 | ||
005 | 20240423125315.0 | ||
007 | cr nn 008mamaa | ||
008 | 200720s2020 sz | s |||| 0|eng d | ||
020 |
_a9783030529628 _9978-3-030-52962-8 |
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024 | 7 |
_a10.1007/978-3-030-52962-8 _2doi |
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050 | 4 | _aQA75.5-76.95 | |
072 | 7 |
_aUYA _2bicssc |
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072 | 7 |
_aCOM014000 _2bisacsh |
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072 | 7 |
_aUYA _2thema |
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082 | 0 | 4 |
_a004.0151 _223 |
100 | 1 |
_aAlexandru, Andrei. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aFoundations of Finitely Supported Structures _h[electronic resource] : _bA Set Theoretical Viewpoint / _cby Andrei Alexandru, Gabriel Ciobanu. |
250 | _a1st ed. 2020. | ||
264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2020. |
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300 |
_aXI, 204 p. 2 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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505 | 0 | _aThe 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 | _aThis 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-fuzzysubsets 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 | _aComputer science. | |
650 | 0 |
_aComputer science _xMathematics. |
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650 | 0 | _aMathematical logic. | |
650 | 1 | 4 | _aTheory of Computation. |
650 | 2 | 4 | _aMathematics of Computing. |
650 | 2 | 4 | _aMathematical Logic and Foundations. |
700 | 1 |
_aCiobanu, Gabriel. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer Nature eBook | |
776 | 0 | 8 |
_iPrinted edition: _z9783030529611 |
776 | 0 | 8 |
_iPrinted edition: _z9783030529635 |
776 | 0 | 8 |
_iPrinted edition: _z9783030529642 |
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-030-52962-8 |
912 | _aZDB-2-SCS | ||
912 | _aZDB-2-SXCS | ||
942 | _cSPRINGER | ||
999 |
_c176525 _d176525 |