In descriptive set theory and related areas of mathematics, a hyperfinite equivalence relation on a standard Borel space X is a Borel equivalence relation E with countable classes, that can, in a certain sense, be approximated by Borel equivalence relations that have finite classes.
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related areas of mathematics, a hyperfiniteequivalencerelation on a standard Borel space X is a Borel equivalencerelation E with countable classes, that...
In mathematics, an equivalencerelation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments...
standard Borel spaces X and Y are Borel-isomorphic iff |X| = |Y|. Hyperfiniteequivalencerelation Wadge hierarchy – levels of complexity for sets of realsPages...
encapsulates various more specific concepts, such as that of a hyperfiniteequivalencerelation, but is of interest in and of itself. A main area of study...
are the hyperfinite type II1 factor and the hyperfinite type II∞ factor, found by Murray & von Neumann (1936). These are the unique hyperfinite factors...
to the order relation ≤ given by the comparison rule below. The numeric forms are placed in equivalence classes; each such equivalence class is a surreal...
R N {\displaystyle \mathbb {R} ^{\mathbb {N} }} by the resulting equivalencerelation is a hyperreal field ∗ R {\displaystyle ^{*}\mathbb {R} } , a situation...
continuous geometry other than projective space was the projections of the hyperfinite type II factor. Menger and Birkhoff gave axioms for projective geometry...
true of hyperreal numbers. The transfer principle concerns the logical relation between the properties of the real numbers R, and the properties of a larger...
A relation is defined on B as follows: (a, b) ~ (c, d) when there is a u in U such that ua = c and ub = d. This relation is in fact an equivalence relation...
Surprisingly enough, there is a consistent way to do it. As a result, the equivalence classes of sequences that differ by some sequence declared zero will...
null sequence becomes an infinitesimal in the sense of an equivalence class modulo a relation defined in terms of a suitable ultrafilter. The article by...
unlimited (infinite) element of *N. These facts can be used to prove the equivalence of the following two conditions for an internal hyperreal-valued function...
Relative to the ultrapower construction of the hyperreal numbers as equivalence classes of sequences ⟨ u n ⟩ {\displaystyle \langle u_{n}\rangle } of...
continuous geometry other than projective space was the projections of the hyperfinite type II factor. In more pure lattice theoretical work, he solved the...
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