Proceedings of the American Mathematical Society

Author(s): Ilijas Farah; Slawomir Solecki
Journal: Proc. Amer. Math. Soc. 131 (2003), 1971-1975.
MSC (2000): Primary 54D55, 06E99
Posted: January 8, 2003
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Abstract: We find two $F_{\sigma\delta}$ ideals on $\mathbb N$ neither of which is $F_\sigma$ whose quotient Boolean algebras are homogeneous but nonisomorphic. This solves a problem of Just and Krawczyk (1984).

1.: B. Balcar, W. G $\l$ ówczynski, and T. Jech.
The sequential topology on complete Boolean algebras.
Fundamenta Mathematicae, 155:59-78, 1998. MR 99b:28006
2.: I. Farah.
Analytic quotients: theory of liftings for quotients over analytic ideals on the integers.
Mem. Amer. Math. Soc., vol. 148, no. 702, 2000.
177 pp. MR 2001c:03076
3.: W. Just and A. Krawczyk.
On certain Boolean algebras ${\mathcal P}(\omega)/I$ .
Transactions of the American Mathematical Society, 285:411-429, 1984. MR 86f:04003
4.: D. Maharam.
An algebraic characterization of measure algebras.
Annals of Mathematics, 48:154-167, 1947. MR 8:321b
5.: S. Solecki.
Analytic ideals and their applications.
Annals of Pure and Applied Logic, 99:51-72, 1999. MR 2000g:03112

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54D55, 06E99

Ilijas Farah
Affiliation: Department of Mathematics, CUNY, Graduate Center and College of Staten Island, Staten Island, New York 10314 -- and -- Matematicki Institut, Kneza Mihaila 35, Belgrade, Serbia
Address at time of publication: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3
Email: ifarah@gc.cuny.edu, ifarah@mathstat.yorku.ca

Slawomir Solecki
Affiliation: Department of Mathematics, 1409 W. Green Street, University of Illinois, Urbana, Illinois 61801
Email: ssolecki@math.uiuc.edu

DOI: 10.1090/S0002-9939-03-06734-0
PII: S 0002-9939(03)06734-0
Received by editor(s): August 27, 2001
Received by editor(s) in revised form: February 8, 2002
Posted: January 8, 2003
Additional Notes: The first author acknowledges support received from the National Science Foundation (USA) via grant DMS-40313-00-01 and from the PSC-CUNY grant \#62785-00-31. The second author was supported by NSF grants DMS-9803676 and DMS-0102254
Communicated by: Alan Dow
Copyright of article: Copyright 2003, American Mathematical Society

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