Nonstandard Analysis, Axiomatically

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

• 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.