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Borel Groups of Low Descriptive Complexity
Author(s) -
ENGELEN FONS
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb36800.x
Subject(s) - mathematics , indecomposable module , zero (linguistics) , hierarchy , class (philosophy) , homogeneous , borel set , pure mathematics , group (periodic table) , descriptive complexity theory , combinatorics , set (abstract data type) , physics , linguistics , computer science , artificial intelligence , philosophy , quantum mechanics , time complexity , economics , market economy , programming language
Let X be a zero‐dimensional first category absolute Borel set of ambiguous class two. Then X can be given the structure of a topological group if and only if X is homogeneous and X = X x X. Thus, within the ambiguous class two, zero‐dimensional groups only occur at the low levels, and the indecomposable levels of the hierarchy of difference classes D α Σ 0 2 in 2 ω .