{"product_id":"incompleteness-in-the-land-of-m-fitting-9781904987345","title":"Incompleteness in the Land of Sets","description":"Russell's paradox arises when we consider those sets that do not belong to themselves. The collection of such sets cannot constitute a set. Step back a bit. Logical formulas define sets (in a standard model). Formulas, being mathematical objects, can be thought of as sets themselves-mathematics reduces to set theory. Consider those formulas that do not belong to the set they define. The collection of such formulas is not definable by a formula, by the same argument that Russell used. This quickly gives Tarski's result on the undefinability of truth. Variations on the same idea yield the famous results of G del, Church, Rosser, and Post. This book gives a full presentation of the basic incompleteness and undecidability theorems of mathematical logic in the framework of set theory. Corresponding results for arithmetic follow easily, and are also given. G del numbering is generally avoided, except when an explicit connection is made between set theory and arithmetic. The book assumes little technical background from the reader. One needs mathematical ability, a general familiarity with formal logic, and an understanding of the completeness theorem, though not its proof. All else is developed and formally proved, from Tarski's Theorem to G del's Second Incompleteness Theorem. Exercises are scattered throughout.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e M. Fitting\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1904987346\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781904987345\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e College Publications\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 02\/19\/2007\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 156\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.50lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.33d","brand":"M. Fitting","offers":[{"title":"Paperback","offer_id":44169914614015,"sku":"9781904987345","price":37.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_9b6a9245-e768-4530-ac4f-016ee4b9d100.jpg?v=1689655659","url":"https:\/\/www.whiterainbookhouse.com\/products\/incompleteness-in-the-land-of-m-fitting-9781904987345","provider":"WR Book House","version":"1.0","type":"link"}