Authors: Farah, Ilijas 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Luzin gaps
Journal: Transactions of the American Mathematical Society
Volume: 356
Issue: 6
First page: 2197
Last page: 2239
Issue Date: 1-Jun-2004
Rank: M21
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-04-03565-2
We isolate a class of F σδ ideals on ℕ that includes all analytic P-ideals and all F σ ideals, and introduce 'Luzin gaps' in their quotients. A dichotomy for Luzin gaps allows us to freeze gaps, and prove some gap preservation results. Most importantly, under PFA all isomorphisms between quotient algebras over these ideals have continuous liftings. This gives a partial confirmation to the author's rigidity conjecture for quotients P(ℕ)/I, We also prove that the ideals NWD(ℚ) and NULL(ℚ) have the Radon-Nikodým property, and (using OCA ∞) a uniformization result for K-coherent families of continuous partial functions.
Publisher: American Mathematical Society
Project: National Science Foundation (USA), Grant DMS-0196153
PSC-CUNY, Grant #62785-00-31

Show full item record


checked on Dec 2, 2023

Page view(s)

checked on Dec 1, 2023

Google ScholarTM




Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.