Nonstandard Analysis, Axiomatically

The book is devoted to nonstandard set theories that serve as foundational basis for nonstandard mathematics. Several popular and some less known nonstandard theories are considered, including internal set theory IST, Hrbacek set theory HST, and others. The book presents the basic structure of the set universe of these theories and methods to effectively develop "applied" nonstandard analysis, metamathematical properties and interrelations of these nonstandard theories between each other and with ZFC and some variants of ZFC, foundational problems of the theories, including the problem of external sets and the Power Set problem, and methods of their solution. The book is oriented towards a reader having some experience in foundations (set theory, model theory) and in nonstandard analysis.

I) Vladimir Kanoveigraduated Moscow State university 1973PhD Moscow State university 1976Doctor of Science in Phys. Math. Moscow Steklov inst. 1986assistant to full professor at Moscow Railroad engineering inst. 1976 - 1998 currently leading researcher at Institute for Information transmissin problems (IITP) Moscowinterests in mathematics: logic and foundations, set theory, nonstandard analysispublications: over 100 papers in Russian and international mathematical journalsII)Michael Reeken PhD in theoretical physics, University of Vienna 1968Research Fellow at the Battelle Institute, Geneva, 1969 - 1972Research grant at the University of Bonn, 1972 - 1974Professor at the University of Bochum, 1972 - 1979Full Professor at the Bergische Universitat Wuppertal since 1979interests in mathematics:problems from mathematical physics, nonlinear functional analysis,nonstandard mathematics, philosophy of mathematics.