E. I. Gordon

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We introduce and discuss a definition of approximation of a topological algebraic system A by finite algebraic systems of some class K. For the case of a discrete algebraic system this definition is equivalent to the well-known definition of a local embedding of an algebraic system A in a class K of algebraic systems. According to this definition A is(More)
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(More)
We develop an axiomatic set theory — the Theory of Hyperfinite Sets THS, which is based on the idea of existence of proper subclasses of big finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS and present some applications.
Introduction. The class of groups which is considered in this paper, namely the class of groups loccally embedded into the class of finite groups (LEF-groups), could appear as a specification of one general definition in model theory [8], but as far as we know, was not considered up to now neither in the group theory, nor in its applications. The first(More)