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Winter 2002 How many Boolean algebras ${\scr P}({\Bbb N})/\scr I$ are there?
Ilijas Farah
Illinois J. Math. 46(4): 999-1033 (Winter 2002). DOI: 10.1215/ijm/1258138463

Abstract

Which pairs of quotients over ideals on $\mathbb{N}$ can be distinguished without assuming additional set theoretic axioms? Essentially, those that are not isomorphic under the Continuum Hypothesis. A CH-diagonalization method for constructing isomorphisms between certain quotients of countable products of finite structures is developed and used to classify quotients over ideals in a class of generalized density ideals. It is also proved that many analytic ideals give rise to quotients that are countably saturated (and therefore isomorphic under CH).

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Ilijas Farah. "How many Boolean algebras ${\scr P}({\Bbb N})/\scr I$ are there?." Illinois J. Math. 46 (4) 999 - 1033, Winter 2002. https://doi.org/10.1215/ijm/1258138463

Information

Published: Winter 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1025.03050
MathSciNet: MR1988247
Digital Object Identifier: 10.1215/ijm/1258138463

Subjects:
Primary: 03E50
Secondary: 06E05

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 4 • Winter 2002
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