{"product_id":"studies-in-weak-arithmetics-volume-patrick-czsgielski-9781575866024","title":"Studies in Weak Arithmetics, Volume 1: Volume 1","description":"\u003cp\u003eThe field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. In this volume, after a general presentation of weak arithmetics, the following topics are studied: the properties of integers of a real closed field equipped with exponentiation; conservation results for the induction schema restricted to first-order formulas with a finite number of alternations of quantifiers; a survey on a class of tools called pebble games; the fact that the reals \u003ci\u003ee\u003c\/i\u003e and pi have approximations expressed by first-order formulas using bounded quantifiers; properties of infinite pictures depending on the universe of sets used; a language that simulates in a sufficiently nice manner all algorithms of a certain restricted class; the logical complexity of the axiom of infinity in some variants of set theory without the axiom of foundation; and the complexity to determine whether a trace is included in another one.\u003cb\u003e\u003c\/b\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Patrick Cégielski\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1575866021\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781575866024\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Center for the Study of Language and Informat\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/15\/2009\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 221\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback","brand":"Patrick Cégielski","offers":[{"title":"Paperback","offer_id":48447922209023,"sku":"9781575866024","price":40.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_5ffcf281-2426-4841-ba42-3d4f16ff843c.jpg?v=1777235722","url":"https:\/\/www.whiterainbookhouse.com\/products\/studies-in-weak-arithmetics-volume-patrick-czsgielski-9781575866024","provider":"WR Book House","version":"1.0","type":"link"}