{"product_id":"the-largest-suslin-axiom-hardback-9781009520713","title":"The Largest Suslin Axiom (Hardback) 9781009520713","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Largest Suslin Axiom\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA thorough study of the minimal model of the Largest Suslin Axiom, including the first proof of its consistency.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eGrigor Sargsyan (Author), Nam Trang (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009520713, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 27 June 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e404 pages\u003cbr\u003e22.9 x 15.2 x 2.7 cm, 0.692 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\"\u003eDeveloping the theory up to the current state-of-the art, this book studies the minimal model of the Largest Suslin Axiom (LSA), which is one of the most important determinacy axioms and features prominently in Hugh Woodin's foundational framework known as the Ultimate L. The authors establish the consistency of LSA relative to large cardinals and develop methods for building models of LSA from other foundational frameworks such as Forcing Axioms. The book significantly advances the Core Model Induction method, which is the most successful method for building canonical inner models from various hypotheses. Also featured is a proof of the Mouse Set Conjecture in the minimal model of the LSA. It will be indispensable for graduate students as well as researchers in mathematics and philosophy of mathematics who are interested in set theory and in particular, in descriptive inner model theory.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction\u003cbr\u003e 2. Hybrid J-structures\u003cbr\u003e 3. Short tree strategy mice\u003cbr\u003e 4. A comparison theory of HOD mice\u003cbr\u003e 5. HOD mice revisited\u003cbr\u003e 6. The internal theory of LSA HOD mice\u003cbr\u003e 7. Analysis of HOD\u003cbr\u003e 8. Models of LSA as derived models\u003cbr\u003e 9. Condensing sets\u003cbr\u003e 10. Applications\u003cbr\u003e 11. A proof of square in LSA-small HOD mice\u003cbr\u003e 12. LSA from PFA\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52415628345624,"sku":"9781009520713","price":93.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009520713i.jpg?v=1784419637","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-largest-suslin-axiom-hardback-9781009520713","provider":"Freshly Printed Books","version":"1.0","type":"link"}