Illinois Journal of Mathematics

How many Boolean algebras ${\scr P}({\Bbb N})/\scr I$ are there?

Ilijas Farah

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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).

Article information

Illinois J. Math., Volume 46, Number 4 (2002), 999-1033.

First available in Project Euclid: 13 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E50: Continuum hypothesis and Martin's axiom [See also 03E57]
Secondary: 06E05: Structure theory


Farah, Ilijas. How many Boolean algebras ${\scr P}({\Bbb N})/\scr I$ are there?. Illinois J. Math. 46 (2002), no. 4, 999--1033. doi:10.1215/ijm/1258138463.

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