|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||Abstract:||
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
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