Skip to main content Accessibility help
×
Home

New Radon–Nikodym ideals

  • Vladimir Kanovei (a1) and Michael Reeken (a2)

Abstract

Farah recently proved that many Borel P-ideals. on satisfy the following requirement: any measurable homomorphism has a continuous lifting which is a homomorphism itself. Ideals having such a property were called Radon–Nikodym (RN) ideals. Answering some Farah's questions, it is proved that many non-P ideals, including, for instance, Fin ⊗ Fin, are Radon–Nikodym. To prove this result, another property of ideals called the Fubini property, is introduced, which implies RN and is stable under some important transformations of ideals.

Copyright

References

Hide All
1.Farah, I.. Completely additive liftings. Bull. Symb. Logic 4 (1998), 3754.
2.Farah, I.. Liftings of homoraorphisms between quotient structures and Ulam stability. In eds. Buss, S.et al, Logic Colloquium 98 Lecture Notes in Logic, 13 (1998), 173196.
3.Farah, I.. Analytic quotients: theory of liftings for quotients over analytic ideals on the integers. Memoirs Amer. Math. Soc., 148 (2000), 177 pp..
4.Farah, I.. Approximate homomorphisms II: Group homomorphisms. Combinatorica, 20 (2000), 3760.
5.Kanovei, V. and Reeken, M.. On Borel automorphisms of the reals modulo a countable group. Math. Logic Quarterly, 46 (2000), 377384.
6.Kanovei, V. and Reeken, M.. On Ulam's problem of stability of approximate homomorphisms. Proc. Moscow Sleklov Math. Inst. MIAN, 231 (2000), 249283.
7.Kechris, A. S.. Classical Descriptive Set Theory, Graduate Texts in Mathematics, 156 (Springer, 1995).
8.Kechris, A. S.. Rigidity properties of Borel ideals on the integers. Topology and Applications, 85 (1998), 195205.
9.Todorcevic, S.. Analytic gaps. Fund. Math., 150 (1996), 5566.
10.Velickovic, B.. Definable automorphisms of Proc. Amer. Math. Soc. 96 (1986), pp. 130135.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

MSC classification

Related content

Powered by UNSILO

New Radon–Nikodym ideals

  • Vladimir Kanovei (a1) and Michael Reeken (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.