{"product_id":"intuitive-axiomatic-set-theory-hardcover","title":"Intuitive Axiomatic Set Theory - Hardcover","description":"\u003cp\u003eby \u003cb\u003eJosé L. Garciá\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eSet theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable.\u003c\/p\u003e\u003cp\u003eThe book has two parts. The first one presents, from the sole intuition of \"collection\" and \"object\", the axiomatic ZFC-theory. Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes.\u003c\/p\u003e\u003cp\u003eThe second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic.\u003c\/p\u003e\u003cp\u003eThe book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.\u003c\/p\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eJosé Luis García\u003c\/strong\u003e is Emeritus Professor at the University of Murcia, Spain. He began his study of Mathematics at the University of Granada (Spain). After several years teaching Mathematics in secondary school, he was enrolled by the University of Murcia (Spain) as a member of the group working on algebra, led by Professor Gomez Pardo. He received his doctorate and a permanent position at the same university. He developed his research on Ring and Module Theory. He became full professor in 1991, and then served for thirty years.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 346\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.81 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e April 04, 2024\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":51750211584288,"sku":"9781032581200","price":187.9,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0974\/9764\/5344\/files\/bf148ba54fe1a7f94a3f27970e66aa36.webp?v=1779945994","url":"https:\/\/ebocreations.com\/products\/intuitive-axiomatic-set-theory-hardcover","provider":"The E-Book Oasis LLC","version":"1.0","type":"link"}