{"product_id":"9789814571593","title":"Notes On Forcing Axioms","description":"\u003cp\u003eIn the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behind a number of fundamental results such as the Open Mapping Theorem or the Banach–Steinhaus Boundedness Principle. This volume brings the Baire category method to another level of sophistication via the internal version of the set-theoretic forcing technique. It is the first systematic account of applications of the higher forcing axioms with the stress on the technique of building forcing notions rather than on the relationship between different forcing axioms or their consistency strengths.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eBaire Category Theorem and the Baire Category Numbers\u003c\/li\u003e\n\u003cli\u003eCoding Sets by the Real Numbers\u003c\/li\u003e\n\u003cli\u003eConsequences in Descriptive Set Theory\u003c\/li\u003e\n\u003cli\u003eConsequences in Measure Theory\u003c\/li\u003e\n\u003cli\u003eVariations on the Souslin Hypothesis\u003c\/li\u003e\n\u003cli\u003eThe \u003ci\u003eS\u003c\/i\u003e-Spaces and the \u003ci\u003eL\u003c\/i\u003e-Spaces\u003c\/li\u003e\n\u003cli\u003eThe Side-condition Method\u003c\/li\u003e\n\u003cli\u003eIdeal Dichotomies\u003c\/li\u003e\n\u003cli\u003eCoherent and Lipschitz Trees\u003c\/li\u003e\n\u003cli\u003eApplications to the \u003ci\u003eS\u003c\/i\u003e-Space Problem and the von Neumann Problem\u003c\/li\u003e\n\u003cli\u003eBiorthogonal Systems\u003c\/li\u003e\n\u003cli\u003eStructure of Compact Spaces\u003c\/li\u003e\n\u003cli\u003eRamsey Theory on Ordinals\u003c\/li\u003e\n\u003cli\u003eFive Cofinal Types\u003c\/li\u003e\n\u003cli\u003eFive Linear Orderings\u003c\/li\u003e\n\u003cli\u003eCardinal Arithmetic and mm\u003c\/li\u003e\n\u003cli\u003eReflection Principles\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003e\u003ci\u003eAppendices:\u003c\/i\u003e\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eBasic Notions\u003c\/li\u003e\n\u003cli\u003ePreserving Stationary Sets\u003c\/li\u003e\n\u003cli\u003eHistorical and Other Comments\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Graduate students and researchers in logic, set theory and  related fields.\u003cbr\u003e\u003cb\u003eKey Features:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eThis is a first systematic exposition of the unified approach for building proper, semi-proper, and stationary preserving forcing notions through the method of using elementary submodels as side conditions\u003c\/li\u003e\n\u003cli\u003eThe books starts from the classical applications of Martin's axioms and ends with some of the most sophisticated applications of the Proper Forcing Axioms. In this way, the reader is led into a natural process of understanding the combinatorics hidden behind the method\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47144683307248,"sku":"9789814571593","price":30.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814571593_p0.jpg?v=1763691042","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814571593","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}