{"product_id":"9781575866024","title":"Studies in Weak Arithmetics","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\u003cp\u003e\u003c\/p\u003e","brand":"Center for the Study of Language and Inf","offers":[{"title":"Default Title","offer_id":47056047309040,"sku":"9781575866024","price":36.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781575866024_p0.jpg?v=1763793918","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781575866024","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}