Illinois Journal of Mathematics

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

Ilijas Farah

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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).

Article information

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

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138463

Digital Object Identifier
doi:10.1215/ijm/1258138463

Mathematical Reviews number (MathSciNet)
MR1988247

Zentralblatt MATH identifier
1025.03050

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

Citation

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. https://projecteuclid.org/euclid.ijm/1258138463


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