{"product_id":"9781461369325","title":"Siberian School of Algebra and Logic","description":"\u003ch1\u003eSiberian School of Algebra and Logic\u003c\/h1\u003e \u003ch2\u003eErshov, Yuri L.\u003c\/h2\u003e \u003cp\u003eThe theory of constructive (recursive) models follows from  works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and  Vaught in the 50s. Within the framework of this theory, algorithmic  properties of abstract models are investigated by constructing  representations on the set of natural numbers and studying relations  between algorithmic and structural properties of these models. \u003cbr\u003e  This book is a very readable exposition of the modern theory of  constructive models and describes methods and approaches developed by  representatives of the Siberian school of algebra and logic and some  other researchers (in particular, Nerode and his colleagues). The main  themes are the existence of recursive models and applications to  fields, algebras, and ordered sets (Ershov), the existence of  decidable prime models (Goncharov, Harrington), the existence of  decidable saturated models (Morley), the existence of decidable  homogeneous models (Goncharov and Peretyat'kin), properties of the  Ehrenfeucht theories (Millar, Ash, and Reed), the theory of  algorithmic dimension and conditions of autostability (Goncharov, Ash,  Shore, Khusainov, Ventsov, and others), and the theory of computable  classes of models with various properties. \u003cbr\u003e  Future perspectives of the theory of constructive models are also  discussed. Most of the results in the book are presented in monograph  form for the first time. \u003cbr\u003e  The theory of constructive models serves as a basis for recursive  mathematics. It is also useful in computer science, in particular, in  the study of programming languages, higher level languages of  specification, abstract data types, and problems of synthesis and  verification of programs. Therefore, the book will be useful for not  only specialists in mathematical logic and the theory of algorithms  but also for scientists interested in the mathematical fundamentals of  computer science. \u003cbr\u003e  The authors are eminent specialists in mathematical logic. They haveestablished fundamental results on elementary theories, model theory,  the theory of algorithms, field theory, group theory, applied logic,  computable numberings, the theory of constructive models, and the  theoretical computer science.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-09-28\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781461369325\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4615-4305-3\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 293\u003c\/p\u003e ","brand":"Springer US","offers":[{"title":"Default Title","offer_id":46265534972044,"sku":"9781461369325","price":197.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781461369325.jpg?v=1775710595","url":"https:\/\/lateknightbooks.com\/products\/9781461369325","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}