04578nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001300172072001600185072002300201072001500224100008300239245011200322250001800434264007500452300004400527336002600571337002600597338003600623347002400659490005900683505096100742520171101703650003603414650003103450650004803481650001803529650002403547650003803571650004703609650004403656650001803700650004003718710003403758773002603792776003603818776003603854830006603890856004603956912001404002912001504016999001704031978-3-031-56215-0DE-He21320251030111824.0cr nn 008mamaa240418s2024    sz |    s    |||| 0|eng d  a97830315621509978-3-031-56215-07 a10.1007/978-3-031-56215-02doi 4aQA8-10.4 7aPBB2bicssc 7aMAT0150002bisacsh 7aPBB2thema1 aKossak, Roman.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97537010aMathematical Logich[electronic resource] :bOn Numbers, Sets, Structures, and Symmetry /cby Roman Kossak.  a2nd ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXVI, 257 p. 29 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Graduate Texts in Philosophy,x2627-6054 ;v40 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.  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. . 0aMathematicsxPhilosophy.969649 0aMathematical logic.966195 0aComputer arithmetic and logic units.975371 0aLogic.970674 0aMathematics.96552314aPhilosophy of Mathematics.96965024aMathematical Logic and Foundations.96619824aArithmetic and Logic Structures.97537224aLogic.97067424aApplications of Mathematics.9655292 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303156214308iPrinted edition:z9783031562167 0aSpringer Graduate Texts in Philosophy,x2627-6054 ;v497537340uhttps://doi.org/10.1007/978-3-031-56215-0  aZDB-2-REP  aZDB-2-SXPR  c59210d59210