## Illinois Journal of Mathematics

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

Ilijas Farah

#### 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

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
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