{"product_id":"simple-theories-and-hyperimaginaries-hardback-9780521119559","title":"Simple Theories and Hyperimaginaries (Hardback) 9780521119559","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSimple Theories and Hyperimaginaries\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis book is a self-contained, up-to-date introduction to simple theories and the model theory of hyperimaginaries.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eEnrique Casanovas (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521119559, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 30 June 2011\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e184 pages\u003cbr\u003e23.3 x 15.5 x 1.5 cm, 0.38 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\"\u003eThis book is an up-to-date introduction to simple theories and hyperimaginaries, with special attention to Lascar strong types and elimination of hyperimaginary problems. Assuming only knowledge of general model theory, the foundations of forking, stability and simplicity are presented in full detail. The treatment of the topics is as general as possible, working with stable formulas and types and assuming stability or simplicity of the theory only when necessary. The author offers an introduction to independence relations as well as a full account of canonical bases of types in stable and simple theories. In the last chapters the notions of internality and analyzability are discussed and used to provide a self-contained proof of elimination of hyperimaginaries in supersimple theories.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Preliminaries\u003cbr\u003e 2. ?-types, stability and simplicity\u003cbr\u003e 3. ?-types and the local rank D(?, ?, k)\u003cbr\u003e 4. Forking\u003cbr\u003e 5. Independence\u003cbr\u003e 6. The local rank CB?(?)\u003cbr\u003e 7. Heirs and coheirs\u003cbr\u003e 8. Stable forking\u003cbr\u003e 9. Lascar strong types\u003cbr\u003e 10. The independence theorem\u003cbr\u003e 11. Canonical bases\u003cbr\u003e 12. Abstract independence relations\u003cbr\u003e 13. Supersimple theories\u003cbr\u003e 14. More ranks\u003cbr\u003e 15. Hyperimaginaries\u003cbr\u003e 16. Hyperimaginary forking\u003cbr\u003e 17. Canonical bases revisited\u003cbr\u003e 18. Elimination of hyperimaginaries\u003cbr\u003e 19. Orthogonality and analysability\u003cbr\u003e 20. Hyperimaginaries in supersimple theories.\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]\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":46005141143832,"sku":"9780521119559","price":106.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521119559i_c24ac9b6-bb2e-41f3-ba3c-696136275d5d.jpg?v=1691371645","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/simple-theories-and-hyperimaginaries-hardback-9780521119559","provider":"Freshly Printed Books","version":"1.0","type":"link"}