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020 _a9783031562150
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024 7 _a10.1007/978-3-031-56215-0
_2doi
050 4 _aQA8-10.4
072 7 _aPBB
_2bicssc
072 7 _aMAT015000
_2bisacsh
072 7 _aPBB
_2thema
100 1 _aKossak, Roman.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_975370
245 1 0 _aMathematical Logic
_h[electronic resource] :
_bOn Numbers, Sets, Structures, and Symmetry /
_cby Roman Kossak.
250 _a2nd ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXVI, 257 p. 29 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,
_x2627-6054 ;
_v4
505 0 _aPart I: Logic, Sets, and Numbers -- Chapter 1. First-order Logic -- Chapter 2. Logical seeing -- Chapter 3. What is a Number? -- Chapter 4. Seeing the Number Structures -- Chapter 5. Points, Lines, and the Structure of R -- Chapter 6. Set Theory -- Part II: Relations, Structures, Geometry -- Chapter 7. Relations -- Chapter 8. Definable Elements and Constants -- Chapter 9. Minimal and Order-Minimal Structures -- Chapter 10. Geometry of Definable Sets -- Chapter 11. Where Do Structures Come From? -- Chapter 12. Elementary Extensions and Symmetries -- Chapter 13. Tame vs. Wild -- Chapter 14. First-Order Properties -- Chapter 15. Symmetries and Logical Visibility One More Time -- Part III: Inference, Models, Categoricity and Diversity -- Chapter 16. Logical Inference -- Chapter 17. Categoricity -- Chapter 18. Counting Countable Models -- Chapter 19. Infinitary Logics -- Chapter 20. Symmetry and Definability -- Appendices -- Bibliography -- Index.
520 _aThis textbook is a second edition of the successful, Mathematical Logic: On Numbers, Sets, Structures, and Symmetry. It retains the original two parts found in the first edition, while presenting new material in the form of an added third part to the textbook. The textbook offers a slow introduction to mathematical logic, and several basic concepts of model theory, such as first-order definability, types, symmetries, and elementary extensions. Part I, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics. 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. The added Part III to the book is closer to what one finds in standard introductory mathematical textbooks. Definitions, theorems, and proofs that are introduced are still preceded by remarks that motivate the material, but the exposition is more formal, and includes more advanced topics. The focus is on the notion of countable categoricity, which analyzed in detail using examples from the first two parts of the book. This textbook is suitable for graduate students in mathematical logic and set theory and 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
_xPhilosophy.
_969649
650 0 _aMathematical logic.
_966195
650 0 _aComputer arithmetic and logic units.
_975371
650 0 _aLogic.
_970674
650 0 _aMathematics.
_965523
650 1 4 _aPhilosophy of Mathematics.
_969650
650 2 4 _aMathematical Logic and Foundations.
_966198
650 2 4 _aArithmetic and Logic Structures.
_975372
650 2 4 _aLogic.
_970674
650 2 4 _aApplications of Mathematics.
_965529
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031562143
776 0 8 _iPrinted edition:
_z9783031562167
830 0 _aSpringer Graduate Texts in Philosophy,
_x2627-6054 ;
_v4
_975373
856 4 0 _uhttps://doi.org/10.1007/978-3-031-56215-0
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