{"product_id":"9781402006609","title":"Trends in Logic: A Categorical Approach to Nonclassical Propositional Logics","description":"\u003ch1\u003eTrends in Logic: A Categorical Approach to Nonclassical Propositional Logics\u003c\/h1\u003e \u003ch2\u003eGhilardi, Silvio; Zawadowski, M.\u003c\/h2\u003e \u003cp\u003eThis book is an example of fruitful interaction between (non-classical) propo­ sitionallogics and (classical) model theory which was made possible due to categorical logic. Its main aim consists in investigating the existence of model­ completions for equational theories arising from propositional logics (such as the theory of Heyting algebras and various kinds of theories related to proposi­ tional modal logic ). The existence of model-completions turns out to be related to proof-theoretic facts concerning interpretability of second order propositional logic into ordinary propositional logic through the so-called 'Pitts' quantifiers' or 'bisimulation quantifiers'. On the other hand, the book develops a large number of topics concerning the categorical structure of finitely presented al­ gebras, with related applications to propositional logics, both standard (like Beth's theorems) and new (like effectiveness of internal equivalence relations, projectivity and definability of dual connectives such as difference). A special emphasis is put on sheaf representation, showing that much of the nice categor­ ical structure of finitely presented algebras is in fact only a restriction of natural structure in sheaves. Applications to the theory of classifying toposes are also covered, yielding new examples. The book has to be considered mainly as a research book, reporting recent and often completely new results in the field; we believe it can also be fruitfully used as a complementary book for graduate courses in categorical and algebraic logic, universal algebra, model theory, and non-classical logics. 1.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2002-07-31\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9781402006609\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-015-9936-8\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 245\u003c\/p\u003e ","brand":"Springer Netherlands","offers":[{"title":"Default Title","offer_id":46541615038604,"sku":"9781402006609","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781402006609.jpg?v=1775742645","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781402006609","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}