{"product_id":"studies-in-weak-arithmetics-volume-1-volume-1-lecture-notes-1575866021","title":"Studies in Weak Arithmetics, Volume 1 (Volume 1) (Lecture Notes)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 1575866021\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e C\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\u003c\/p\u003e\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 e 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.\u003c\/p\u003e","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":51327003263264,"sku":"NEW1575866021","price":45.56,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/61f55Cxw0XL.jpg?v=1773163452","url":"https:\/\/miakarts.com\/products\/studies-in-weak-arithmetics-volume-1-volume-1-lecture-notes-1575866021","provider":"Miakarts Books","version":"1.0","type":"link"}