Nonstandard Methods and Applications in Mathematics

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-fifth publication in the Lecture Notes in Logic series, grew from a conference on Nonstandard Methods and Applications in Mathematics held in Pisa, Italy from 12{u2013}16 June, 2002. It contains ten peer-reviewed papers that aim to provide something more timely than a textbook, but less ephemeral than a conventional proceedings. Nonstandard analysis is one of the great achievements of modern applied mathematical logic. These articles consider the foundations of the subject, as well as its applications to pure and applied mathematics and mathematics education Contents Preface FOUNDATIONS The eightfold path to nonstandard analysis Neoclosed forcing Nonstandard objects in set theory PURE MATHEMATICS The microscopic behavior of measurable functions Nonstandard measure constructions — solutions and problems Inverse problem for upper asymptotic density II Nonstandard analysis and cohomology APPLIED MATHEMATICS Loeb space methods for stochastic Navier-Stokes equations Discrete approximation of compact operators and approximation of their spectra TEACHING Nonstandard analysis at pre-university level: Naive magnitude analysis