Salbany, S. and T. Todorov, Nonstandard and standard cornpactifications of ordered topological spaces, Topology and its Applications 47 (1992) 35-52. We construct the Nachbin ordered compactification and the ordered realcornpactification, a notion defined in the paper, of a given ordered topological space as nonstandard ordered hulls. The maximal ideals in the algebras of the differences of mon...

First order reasoning about hyperintegers can prove things about sets of integers. In the author’s paper Nonstandard Arithmetic and Reverse Mathematics, Bulletin of Symbolic Logic 12 (2006), it was shown that each of the “big five” theories in reverse mathematics, including the base theory RCA0, has a natural nonstandard counterpart. But the counterpart RCA0 of RCA0 has a defect: it does not im...

Some important concepts in the nonstandard analysis theory of turbulence are presented in this article. The structure of point, on which differential equations are defined, is analyzed. The distinction between the uniform point and the non-uniform point, as well as between the standard point and the nonstandard point, is showed. A new kind of equations, which differ essentially from those in ex...

Jean Kimmel gratefully acknowledges institutional support from the W.E. Upjohn Institute for Employment Research. We are deeply indebted to Wei-Jang Huang for her superb research assistance. Also, we thank Nancy Mack for quality secretarial support and Linda Richer for library research. Lisa Powell gratefully acknowledges funding from the Social Sciences and Humanities Research Council of Canad...

Recently, the second author, Briseid and Safarik introduced nonstandard Dialectica, a functional interpretation that is capable of eliminating instances of familiar principles of nonstandard arithmetic including overspill, underspill, and generalisations to higher types from proofs. We show that, under few metatheoretical assumptions, the properties of this interpretation are mirrored by first ...

In this article we aim to return labor (particularly the most vulnerable members of the labor market) to the core of the comparative political economy of advanced democracies. We formulate a framework with which to conceptualize cheap labor in advanced democracies. We propose that to understand the politics of cheap labor, the weakest members of the labor market need to be divided into two stru...

Nonstandard analysis is the branch of mathematics concerned with constructing a number system that includes infinitesimals. These are numbers smaller than any real number yet still greater than zero. Although nonstandard analysis was developed in 1966 by Abraham Robinson, it is based off of Gottfried Wilhelm Leibniz’s construction of the calculus, created some 300 years earlier. Nonstandard ana...