Two $F_{\sigma \delta }$ ideals
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- by Ilijas Farah and Sławomir Solecki PDF
- Proc. Amer. Math. Soc. 131 (2003), 1971-1975 Request permission
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).References
- Bohuslav Balcar, Wiesław Główczyński, and Thomas Jech, The sequential topology on complete Boolean algebras, Fund. Math. 155 (1998), no. 1, 59–78. MR 1487988, DOI 10.4064/fm183-1-4
- Ilijas Farah, Analytic quotients: theory of liftings for quotients over analytic ideals on the integers, Mem. Amer. Math. Soc. 148 (2000), no. 702, xvi+177. MR 1711328, DOI 10.1090/memo/0702
- Winfried Just and Adam Krawczyk, On certain Boolean algebras ${\scr P}(\omega )/I$, Trans. Amer. Math. Soc. 285 (1984), no. 1, 411–429. MR 748847, DOI 10.1090/S0002-9947-1984-0748847-1
- A. R. Collar, On the reciprocation of certain matrices, Proc. Roy. Soc. Edinburgh 59 (1939), 195–206. MR 8, DOI 10.1017/S0370164600012281
- Sławomir Solecki, Analytic ideals and their applications, Ann. Pure Appl. Logic 99 (1999), no. 1-3, 51–72. MR 1708146, DOI 10.1016/S0168-0072(98)00051-7
Additional Information
- 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
- MR Author ID: 350129
- Email: ifarah@gc.cuny.edu, ifarah@mathstat.yorku.ca
- Sławomir Solecki
- Affiliation: Department of Mathematics, 1409 W. Green Street, University of Illinois, Urbana, Illinois 61801
- Email: ssolecki@math.uiuc.edu
- Received by editor(s): August 27, 2001
- Received by editor(s) in revised form: February 8, 2002
- Published electronically: 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 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1971-1975
- MSC (2000): Primary 54D55, 06E99
- DOI: https://doi.org/10.1090/S0002-9939-03-06734-0
- MathSciNet review: 1955288