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020 _a9783319972985
_9978-3-319-97298-5
024 7 _a10.1007/978-3-319-97298-5
_2doi
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072 7 _aPBB
_2bicssc
072 7 _aMAT015000
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072 7 _aPBB
_2thema
082 0 4 _a510.1
_223
100 1 _aKossak, Roman.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMathematical Logic
_h[electronic resource] :
_bOn Numbers, Sets, Structures, and Symmetry /
_cby Roman Kossak.
250 _a1st ed. 2018.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2018.
300 _aXIII, 186 p. 28 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Graduate Texts in Philosophy,
_x2627-6046 ;
_v3
505 0 _aChapter1. Mathematical Logic -- Chapter2. Logical Seeing -- Chapter3. What is a Number? -- Chapter4. Number Structures -- Chapter5. Points, Lines -- Chapter6. Set Theory -- Chapter7. Relations -- Chapter8. Definable Elements and Constants -- Chapter9. Minimal and Order-Minimal Structures -- Chapter10. Geometry of Definable Sets -- Chapter11. Where Do Structures Come From? -- Chapter12. Elementary Extensions and Symmetries -- Chapter13. Tame vs. Wild -- Chapter14. First-order Properties -- Chapter15. Symmetries and Logical Visibility One More Time. .
520 _aThis book, presented in two parts, offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. The exposition does not assume any prerequisites; it is rigorous, but as informal as possible. All necessary concepts are introduced exactly as they would be in a course in mathematical logic; but are accompanied by more extensive introductory remarks and examples to motivate formal developments. The second part, Relations, Structures, Geometry, introduces several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions, and shows how they are used to study and classify mathematical structures. Although more advanced, this second part is accessible to the reader who is either already familiar with basic mathematical logic, or has carefully read the first part of the book. Classical developments in model theory, including the Compactness Theorem and its uses, are discussed. Other topics include tameness, minimality, and order minimality of structures. The book can be used as an introduction to model theory, but unlike standard texts, it does not require familiarity with abstract algebra. This book will also be of interest to mathematicians who know the technical aspects of the subject, but are not familiar with its history and philosophical background.
650 0 _aMathematics—Philosophy.
650 0 _aMathematical logic.
650 0 _aArithmetic and logic units, Computer.
650 0 _aLogic.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 1 4 _aPhilosophy of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/E34020
650 2 4 _aMathematical Logic and Foundations.
_0http://scigraph.springernature.com/things/product-market-codes/M24005
650 2 4 _aArithmetic and Logic Structures.
_0http://scigraph.springernature.com/things/product-market-codes/I12026
650 2 4 _aLogic.
_0http://scigraph.springernature.com/things/product-market-codes/E16000
650 2 4 _aApplications of Mathematics.
_0http://scigraph.springernature.com/things/product-market-codes/M13003
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319972978
776 0 8 _iPrinted edition:
_z9783319972992
776 0 8 _iPrinted edition:
_z9783030073312
830 0 _aSpringer Graduate Texts in Philosophy,
_x2627-6046 ;
_v3
856 4 0 _uhttps://doi.org/10.1007/978-3-319-97298-5
912 _aZDB-2-REP
999 _c17788
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