{"product_id":"godels-theorems-and-zermelos-axioms-a-firm-foundation-of-mathematics-hardcover","title":"Gödel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eLorenz Halbeisen\u003c\/b\u003e (Author), \u003cb\u003eRegula Krapf\u003c\/b\u003e (Author)\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of G?del's classical completeness and incompleteness theorems. In particular, the book includes a full proof of G?del's second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on Zermelo's axioms, containing also a presentation of G?del's constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. In addition, the corrected, revised and extended second edition now provides detailed solutions to all exercises.\u003c\/p\u003e \u003cp\u003eThe book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eLorenz Halbeisen \u003c\/strong\u003eis Professor of Logic and Set Theory at the ETH Zürich.\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eRegula Krapf \u003c\/strong\u003eis Senior Academic Councilor at the University of Bonn since 2023. \u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 342\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.81 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e May 11, 2025\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47572968210653,"sku":"9783031851056","price":122.45,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0811\/9867\/8237\/files\/RQ_dic9c4F9783031851056.webp?v=1773399734","url":"https:\/\/handfulofbooks.com\/products\/godels-theorems-and-zermelos-axioms-a-firm-foundation-of-mathematics-hardcover","provider":"Handful of Books","version":"1.0","type":"link"}