{"product_id":"building-models-by-games-dover-books-on-mathematics-0486450171-used","title":"Building Models by Games (Dover Books on Mathematics)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 0486450171\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Wilfrid Hodges\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e Used\u003c\/p\u003e\u003cp\u003eThis volume presents research by algebraists and model theorists in accessible form for advanced undergraduates or beginning graduate students studying algebra, logic, or model theory. It introduces a general method for building infinite mathematical structures and surveys applications in algebra and model theory. A multi-step procedure, the method resembles a two-player game that continues indefinitely. This approach simplifies, motivates, and unifies a wide range of constructions.Starting with an overview of basic model theory, the text examines a variety of algebraic applications, with detailed analyses of existentially closed groups of class 2. It describes the classical model-theoretic form of this method of construction, which is known as \"omitting types,\" \"forcing,\" or the \"Henkin-Orey theorem,\" The final chapters are more specialized, discussing how the idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras and models of arithmetic. More than 160 exercises range from elementary drills to research-related items, with further information and examples.\u003c\/p\u003e","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":67820106088736,"sku":"USED0486450171","price":29.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/91gLklzPzZL.jpg?v=1792194713","url":"https:\/\/miakarts.com\/en-gb\/products\/building-models-by-games-dover-books-on-mathematics-0486450171-used","provider":"Miakarts Books","version":"1.0","type":"link"}