Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-30T17:26:02.326Z Has data issue: false hasContentIssue false

Liftings of Homomorphisms Between Quotient Structures and Ulam Stability

Published online by Cambridge University Press:  31 March 2017

Ilijas Farah
Affiliation:
York University, North York, Canada
Samuel R. Buss
Affiliation:
University of California, San Diego
Petr Hájek
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Pavel Pudlák
Affiliation:
Academy of Sciences of the Czech Republic, Prague
Get access
Type
Chapter
Information
Logic Colloquium '98 , pp. 173 - 196
Publisher: Cambridge University Press
Print publication year: 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. H., Becker and A.S., Kechris. The descriptive set theory of Polish group actions. Cambridge University Press, 1996.
2. M., Bell. an email of October 1997.
3. M., Bell. Two Boolean algebras with extreme cellular and compactness properties. Canadian Journal of Mathematics, XXXV:824–838, 1983.Google Scholar
4. E., Č ech. Probléme. FundamentaMathematicae, 34:332, 1947.
5. A., Connes. Noncommutative geometry. Academic Press, 1994.
6. H.G., Dales and W.H., Woodin. An Introduction to Independence for Analysts, volume 115 of London Mathematical Society Lecture Note Series. Cambridge University Press, 1987.
7. R., Engelking. General Topology. Heldermann, Berlin, 1989.
8. I., Farah. Analytic quotients. Memoirs of the American Mathematical Society, to appear.
9. I., Farah. Embedding partially ordered sets into ωω. Fundamenta Mathematicae, 151:53–95, 1996.Google Scholar
10. I., Farah. Approximate homomorphisms. Combinatorica, 18:335–348, 1998.Google Scholar
11. I., Farah. Approximate homomorphisms II: Group homomorphisms. Combinatorica, to appear.
12. I., Farah. Completely additive liftings. The Bulletin of Symbolic Logic, 4:37–54, 1998.Google Scholar
13. D., H. Fremlin. Measure algebras. In D., Monk and R., Bonnett, editors, Handbook of Boolean algebras, pages 877–980. Elsevier, 1989.
14. F., Galvin. On a problem of Čech. Notices of the American Mathematical Society, 25:A–604, 1978.Google Scholar
15. G., Hjorth and A.S., Kechris. New dichotomies for Borel equivalence relations. The Bulletin of Symbolic Logic, 3:329–346, 1997.Google Scholar
16. G., Hjorth, A.S., Kechris, and A., Louveau. Borel equivalence relations induced by actions of the symmetric group. Annals of pure and applied logic, 92:63–112, 1998.Google Scholar
17. A., Ionescu Tulcea and C., Ionescu Tulcea. Topics in the theory of lifting. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48. Springer-Verlag, New York, 1969.
18. S.-A., Jalali-Naini. The monotone subsets of Cantor space, filters and descriptive set theory. PhD thesis, Oxford, 1976.
19. W., Just. The space (ω*)n+1 is not always a continuous image of (∗)n. Fundamenta Mathematicae, 132:59–72, 1989.Google Scholar
20. W., Just. A modification of Shelah's oracle chain condition with applications. Transactions of the American Mathematical Society, 329:325–341, 1992.Google Scholar
21. W., Just. A weak version of AT from OCA. Mathematical Science Research Institute Publications, 26:281–291, 1992.Google Scholar
22. N., J. Kalton. The three-space problem for locally bounded F-spaces. Compositio Mathematicae, 37:243–276, 1978.Google Scholar
23. N.J., Kalton. The Maharam problem. Séminaire Initiationàĺ Analyse, 18:1–13, 1988/89.Google Scholar
24. V., Kanovei and M., Reeken. On Baire measurable homomorphisms of quotients of the additive group of the reals. Archive for Mathematical Logic, to appear.
25. A.S., Kechris. Actions of Polish groups and classification problems. preprint.
26. A.S., Kechris. Classical descriptive set theory, volume 156 of Graduate texts in mathematics. Springer, 1995.
27. A.S., Kechris. New directions in descriptive set theory. The Bulletin of Symbolic Logic, 5:161–174, 1999.Google Scholar
28. A., Louveau and B., Velickovic. A note on Borel equivalence relations. Proceedings of the American Mathematical Society, 120:255–259, 1994.Google Scholar
29. A., R.D.Mathias. A remark on rare filters. In A., Hajnal et al., editor, Infinite and finite sets, Vol. III, volume 10 of Coll. Math. Soc. Jänos Bolyai, pages 1095–1097. North Holland, 1975.
30. I.I., Parovičenko. A universal bicompact of weight ℵ1. Soviet Mathematics Doklady, 4:592–592, 1963.Google Scholar
31. R., Price. On a problem of Čech. Topology and Its Applications, 14:319–329, 1982.Google Scholar
32. M., Scheepers. Cardinals of countable cofinality and eventual domination. Order, 11:221–235, 1995.Google Scholar
33. S., Shelah. Proper Forcing. Lecture Notes in Mathematics 940. Springer, 1982.
34. S., Solecki. Analytic ideals. The Bulletin of Symbolic Logic, 2:339–348, 1996.Google Scholar
35. S., Solecki. Analytic ideals and their applications. preprint, 1996.
36. R., Solovay. A model of set theory in which every set of reals is Lebesgue measurable. Annals of Mathematics, 92:1–56, 1970.Google Scholar
37. M., Talagrand. Compacts de fonctions mesurables et filters nonmesurables. Studia Math., 67:13–43, 1980.Google Scholar
38. M., Talagrand. A new look at independence. Annals of Probability, 24:1–34, 1996.Google Scholar
39. W., Thurston. On proof and progress in mathematics. Bullettin of the American Mathematical Society, 30:161–177, 1994.Google Scholar
40. S., Todorcevic. Partition Problems in Topology, volume 84 of Contemporary mathematics. American Mathematical Society, Providence, Rhode Island, 1989.
41. S., Todorcevic. Analytic gaps. Fundamenta Mathematicae, 150:55–67, 1996.Google Scholar
42. S., Todorcevic. Definable ideals and gaps in their quotients. In C., A. DiPrisco et al, editor, Set Theory: Techniques and Applications, pages 213–226. Kluwer Academic Press, 1997.
43. S., Todorcevic. Gaps in analytic quotients. Fundamenta Mathematicae, 156:85–97, 1998.Google Scholar
44. S.M., Ulam. Problems in modern mathematics. John Wiley & Sons, 1964.
45. S.M., Ulam and D., Mauldin. Mathematical problems and games. Advances in Applied Mathematics, 8:281–344, 1987.Google Scholar
46. E., van Douwen. Mappings from hyperspaces and converging sequences. Topology and its Applications, 34:35–45, 1990.Google Scholar
47. B., Velickovic. Definable automorphisms of P(ω)/Fin. Proceedings of the American Mathematical Society, 96:130–135, 1986.Google Scholar
48. B., Velickovic. OCA and automorphisms of P(ω)/Fin. Topology and its Applications, 49:1–12, 1992.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×