{"product_id":"9783642060779","title":"Nonstandard Analysis, Axiomatically (Springer Monographs in Mathematics)","description":"In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at \"unnatural\" interpretations of the membership relation. 1 Getting started.- 2 Elementary real analysis in the nonstandard universe.- 3 Theories of internal sets.- 4 Metamathematics of internal theories.- 5 Definable external sets and metamathematics of HST.- 6 Partially saturated universes and the Power Set problem.- 7 Forcing extensions of the nonstandard universe.- 8 Other nonstandard theories.- 9 \"Hyperfinite\" descriptive set theory.- References. \u003cp\u003eI) Vladimir Kanovei\u003c\/p\u003e\u003cp\u003egraduated Moscow State university 1973\nPhD Moscow State university 1976\nDoctor of Science in Phys. Math. Moscow Steklov inst. 1986\u003c\/p\u003e\u003cp\u003eassistant to full professor at Moscow Railroad engineering inst. \n1976 - 1998 \u003c\/p\u003e\u003cp\u003ecurrently leading researcher at Institute for Information \ntransmissin problems (IITP) Moscow\u003c\/p\u003e\u003cp\u003einterests in mathematics: \nlogic and foundations, set theory, nonstandard analysis\npublications: \nover 100 papers in Russian and international mathematical journals\u003c\/p\u003e\u003cp\u003eII)\nMichael Reeken \nPhD in theoretical physics, University of Vienna 1968\u003c\/p\u003e\u003cp\u003eResearch Fellow at the Battelle Institute, Geneva, 1969 - 1972\u003c\/p\u003e\u003cp\u003eResearch grant at the University of Bonn, 1972 - 1974\u003c\/p\u003e\u003cp\u003eProfessor at the University of Bochum, 1972 - 1979\u003c\/p\u003e\u003cp\u003eFull Professor at the Bergische Universität Wuppertal since 1979\u003c\/p\u003e\u003cp\u003einterests in mathematics:\nproblems from mathematical physics, nonlinear functional analysis,\nnonstandard mathematics, philosophy of mathematics.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":49662587109624,"sku":"00000_00000_00000_00000","price":215.4,"currency_code":"AUD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/8208\/6904\/files\/9783642060779-1.jpg?v=1784143566","url":"https:\/\/kinokuniya.com.au\/products\/9783642060779","provider":"Books Kinokuniya Australia","version":"1.0","type":"link"}