1.  18
    An Axiomatics for Nonstandard Set Theory, Based on Von Neumann-Bernays-Gödel Theory.P. V. Andreev & E. I. Gordon - 2001 - Journal of Symbolic Logic 66 (3):1321-1341.
    We present an axiomatic framework for nonstandard analysis-the Nonstandard Class Theory (NCT) which extends von Neumann-Gödel-Bernays Set Theory (NBG) by adding a unary predicate symbol St to the language of NBG (St(X) means that the class X is standard) and axioms-related to it- analogs of Nelson's idealization, standardization and transfer principles. Those principles are formulated as axioms, rather than axiom schemes, so that NCT is finitely axiomatizable. NCT can be considered as a theory of definable classes of Bounded Set Theory (...)
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  2.  14
    A Theory of Hyperfinite Sets.P. V. Andreev & E. I. Gordon - 2006 - Annals of Pure and Applied Logic 143 (1):3-19.
    We develop an axiomatic set theory — the Theory of Hyperfinite Sets THS— which is based on the idea of the existence of proper subclasses of large finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS, and present some applications.
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  3.  2
    On Finite Approximations of Topological Algebraic Systems.L. Yu Glebsky, E. I. Gordon & C. Ward Hensen - 2007 - Journal of Symbolic Logic 72 (1):1 - 25.
    We introduce and discuss a concept of approximation of a topological algebraic system A by finite algebraic systems from a given class K. If A is discrete, this concept agrees with the familiar notion of a local embedding of A in a class K of algebraic systems. One characterization of this concept states that A is locally embedded in K iff it is a subsystem of an ultraproduct of systems from K. In this paper we obtain a similar characterization of (...)
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