{"product_id":"classification-theory-second-edition-with-a-new-introduction-9781848904231","title":"Classification Theory. Second Edition with a new introduction","description":"\u003cp\u003eThis book is for readers who have learned about first order logic; Gödel's completeness theorem; the Löwenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories \u003cem\u003eT\u003c\/em\u003e; mainly countable. That is, properties dividing them in some sense between understandable and complicated ones.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThe main test problem is the number of models of \u003cem\u003eT\u003c\/em\u003e of the infinite cardinal l as a function of l. This culminates in the so-called \u003cem\u003emain gap theorem\u003c\/em\u003e saying the number is either maximal or quite small in suitable sense. Toward this, other properties are introduced and investigated, such as being \u003cem\u003estable\u003c\/em\u003e or being \u003cem\u003esuper stable\u003c\/em\u003e, where can we define \u003cem\u003edimension\u003c\/em\u003e and \u003cem\u003eweight\u003c\/em\u003e, particularly for super stable theories.\u003c\/p\u003e\u003cbr\u003e","brand":"College Publications","offers":[{"title":"Default Title","offer_id":51324693676306,"sku":"9781848904231","price":30.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0831\/4771\/8930\/files\/img_53e37272-b08f-47cf-a58c-5408a5923589.jpg?v=1748696399","url":"https:\/\/surprise-castle.myshopify.com\/products\/classification-theory-second-edition-with-a-new-introduction-9781848904231","provider":"Surprise Castle","version":"1.0","type":"link"}