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Hierarchies in φ ‐spaces and applications
Author(s) -
Selivanov Victor L.
Publication year - 2005
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310126
Subject(s) - mathematics , hierarchy , sketch , borel hierarchy , hausdorff space , space (punctuation) , discrete mathematics , algebraic properties , algebraic number , topological space , analytical hierarchy , pure mathematics , algebra over a field , borel measure , mathematical economics , computer science , probability measure , algorithm , mathematical analysis , economics , analytic hierarchy process , market economy , operating system
We establish some results on the Borel and difference hierarchies in φ ‐spaces. Such spaces are the topological counterpart of the algebraic directed‐complete partial orderings. E.g., we prove analogs of the Hausdorff Theorem relating the difference and Borel hierarchies and of the Lavrentyev Theorem on the non‐collapse of the difference hierarchy. Some of our results generalize results of A. Tang for the space Pω . We also sketch some older applications of these hierarchies and present a new application to the question of characterizing the ω ‐ary Boolean operations generating a given level of the Wadge hierarchy from the open sets. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)