{"product_id":"ultrafilters-throughout-mathematics-9781470469610","title":"Ultrafilters Throughout Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePresents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to a wide variety of topics. The first part of the book deals solely with ultrafilters; the second part presents the classical ultraproduct construction.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eUltrafilters and their applications: Ultrafilter basics\u003c\/li\u003e\n\u003cli\u003eArrow's theorem on fair voting\u003c\/li\u003e\n\u003cli\u003eUltrafilters in topology\u003c\/li\u003e\n\u003cli\u003eRamsey theory and combinatorial number theory\u003c\/li\u003e\n\u003cli\u003eFoundational concerns\u003c\/li\u003e\n\u003cli\u003eClassical ultraproducts: Classical ultraproducts\u003c\/li\u003e\n\u003cli\u003eApplicationis to geometry, commutative algebra, and number theory\u003c\/li\u003e\n\u003cli\u003eUltraproducts and saturation\u003c\/li\u003e\n\u003cli\u003eNonstandard analysis\u003c\/li\u003e\n\u003cli\u003eLimit groups\u003c\/li\u003e\n\u003cli\u003eMetric ultraproducts and their applications: Metric ultraproducts\u003c\/li\u003e\n\u003cli\u003eAsymptotic cones and Gromov's theorem\u003c\/li\u003e\n\u003cli\u003eSofic groups\u003c\/li\u003e\n\u003cli\u003eFunctional analysis\u003c\/li\u003e\n\u003cli\u003eAdvanced topics: Does an ultrapower depend on the ultrafilter?\u003c\/li\u003e\n\u003cli\u003eThe Keisler-Shelah theorem\u003c\/li\u003e\n\u003cli\u003eLarge cardinals\u003c\/li\u003e\n\u003cli\u003eAppendices: Logic\u003c\/li\u003e\n\u003cli\u003eSet theory\u003c\/li\u003e\n\u003cli\u003eCategory theory\u003c\/li\u003e\n\u003cli\u003eHints and solutions to selected exercises\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50041342493015,"sku":"9781470469610","price":63.9,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470469610.jpg?v=1740182850","url":"https:\/\/bookcurl.com\/products\/ultrafilters-throughout-mathematics-9781470469610","provider":"Book Curl","version":"1.0","type":"link"}