{"product_id":"the-covering-property-axiom-cpa-a-combinatorial-core-of-the-iterated-perfect-set-model-hardback-9780521839204","title":"The Covering Property Axiom, CPA; A Combinatorial Core of the Iterated Perfect Set Model (Hardback) 9780521839204","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Covering Property Axiom, CPA\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eA Combinatorial Core of the Iterated Perfect Set Model\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThis book explores a new axiom of set theory, which simplifies proofs, provides deeper insight, and leads to new results.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eKrzysztof Ciesielski (Author), Janusz Pawlikowski (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521839204, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 23 August 2004\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e198 pages, 3 b\/w illus.\u003cbr\u003e22.9 x 15.2 x 1.6 cm, 0.46 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\"\u003eHere the authors formulate and explore a new axiom of set theory, CPA, the Covering Property Axiom. CPA is consistent with the usual ZFC axioms, indeed it is true in the iterated Sacks model and actually captures the combinatorial core of this model. A plethora of results known to be true in the Sacks model easily follow from CPA. Replacing iterated forcing arguments with deductions from CPA simplifies proofs, provides deeper insight, and leads to new results. One may say that CPA is similar in nature to Martin's axiom, as both capture the essence of the models of ZFC in which they hold. The exposition is self contained and there are natural applications to real analysis and topology. Researchers who use set theory in their work will find much of interest in this book.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Axiom CPAcube and its consequences: properties (A)-(E)\u003cbr\u003e 2. Games and axiom CPAgame\/cube\u003cbr\u003e 3. Prisms and axioms CPAgame\/prism and CPAprism\u003cbr\u003e 4. CPAprism and coverings with smooth functions\u003cbr\u003e 5. Applications of CPAgame\/prism\u003cbr\u003e 6. CPA and properties (F*) and (G)\u003cbr\u003e 7. CPA in the Sacks model.\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 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":"Default Title","offer_id":46265210732824,"sku":"9780521839204","price":120.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521839204i.jpg?v=1692020572","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-covering-property-axiom-cpa-a-combinatorial-core-of-the-iterated-perfect-set-model-hardback-9780521839204","provider":"Freshly Printed Books","version":"1.0","type":"link"}