{"product_id":"an-invitation-to-model-theory-paperback-9781316615553","title":"An Invitation to Model Theory (Paperback \/ softback) 9781316615553","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAn Invitation to Model Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAn innovative and largely self-contained textbook bringing model theory to an undergraduate audience.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJonathan Kirby (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781316615553, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 18 April 2019\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e194 pages, 5 b\/w illus.\u003cbr\u003e22.7 x 15.1 x 1.2 cm, 0.3 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eModel theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Part I. Languages and Structures: 1. Structures\u003cbr\u003e 2. Terms\u003cbr\u003e 3. Formulas\u003cbr\u003e 4. Definable sets\u003cbr\u003e 5. Substructures and quantifiers\u003cbr\u003e Part II. Theories and Compactness: 6. Theories and axioms\u003cbr\u003e 7. The complex and real fields\u003cbr\u003e 8. Compactness and new constants\u003cbr\u003e 9. Axiomatisable classes\u003cbr\u003e 10. Cardinality considerations\u003cbr\u003e 11. Constructing models from syntax\u003cbr\u003e Part III. Changing Models: 12. Elementary substructures\u003cbr\u003e 13. Elementary extensions\u003cbr\u003e 14. Vector spaces and categoricity\u003cbr\u003e 15. Linear orders\u003cbr\u003e 16. The successor structure\u003cbr\u003e Part IV. Characterising Definable Sets: 17. Quantifier elimination for DLO\u003cbr\u003e 18. Substructure completeness\u003cbr\u003e 19. Power sets and Boolean algebras\u003cbr\u003e 20. The algebras of definable sets\u003cbr\u003e 21. Real vector spaces and parameters\u003cbr\u003e 22. Semi-algebraic sets\u003cbr\u003e Part V. Types: 23. Realising types\u003cbr\u003e 24. Omitting types\u003cbr\u003e 25. Countable categoricity\u003cbr\u003e 26. Large and small countable models\u003cbr\u003e 27. Saturated models\u003cbr\u003e Part VI. Algebraically Closed Fields: 28. Fields and their extensions\u003cbr\u003e 29. Algebraic closures of fields\u003cbr\u003e 30. Categoricity and completeness\u003cbr\u003e 31. Definable sets and varieties\u003cbr\u003e 32. Hilbert's Nullstellensatz\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Set theory [\u003ca title=\"See our other books on Set theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Set%20theory%20%5BPBCH%5D%22\"\u003ePBCH\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Philosophy: logic [\u003ca title=\"See our other books on Philosophy: logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy:%20logic%20%5BHPL%5D%22\"\u003eHPL\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46002370609432,"sku":"9781316615553","price":26.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781316615553i.jpg?v=1696683022","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/an-invitation-to-model-theory-paperback-9781316615553","provider":"Freshly Printed Books","version":"1.0","type":"link"}