Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-25T06:23:13.229Z Has data issue: false hasContentIssue false

Rigidity conjectures

from ARTICLES

Published online by Cambridge University Press:  27 June 2017

René Cori
Affiliation:
Université de Paris VII (Denis Diderot)
Alexander Razborov
Affiliation:
Institute for Advanced Study, Princeton, New Jersey
Stevo Todorčević
Affiliation:
Université de Paris VII (Denis Diderot)
Carol Wood
Affiliation:
Wesleyan University, Connecticut
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Logic Colloquium 2000 , pp. 252 - 271
Publisher: Cambridge University Press
Print publication year: 2005

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]U., Abraham,M., Rubin, and S., Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of N1-dense real order types, Annals of Pure and Applied Logic, vol. 29 (1985), pp. 123–206.
[2]A., Andretta, Notes on descriptive set theory, in preparation, 2000.
[3] C.C., Chang and H.J., Keisler,Model theory, North-Holland, 1973.
[4] J.P.R., Christensen, Some results with relation to the control measure problem,Vector space measures and applications II (R.M., Aron and S., Dineen, editors), Lecture Notes in Mathematics, vol. 645, Springer, 1978, pp. 27–34.
[5]I., Farah, Cauchy nets and open colorings,Publications. Institut Mathematique. Nouvelle Serie, vol. 64(78) (1998), pp. 146–152, 50th anniversary of the Mathematical Institute, Serbian Academy of Sciences and Arts (Belgrade, 1996).
[6] I., Farah, Completely additive liftings, The Bulletin of Symbolic Logic, vol. 4 (1998), pp. 37–54.
[7] I., Farah, Analytic quotients: theory of liftings for quotients over analytic ideals on the integers, Memoirs of the American Mathematical Society, vol. 148, (2000), no. 702, 177 pp.öGoogle Scholar
[8] I., Farah, Liftings of homomorphisms between quotient structures and Ulam stability,Logic colloquium '98 (S., Buss, P., Hájek, and P., Pudlák, editors), Lecture notes in logic, vol. 13, A.K.Peters, 2000, pp. 173–196.
[9] I., Farah, How many Boolean algebras P(N)/I are there?, Illinois Journal of Mathematics, vol. 46 (2003), pp. 999–1033.Google Scholar
[10] I., Farah, Luzin gaps, Transactions of the AmericanMathematical Society, vol. 356 (2004), pp. 2197–2239.Google Scholar
[11]I., Farah and S., Solecki, Two Fideals, Proceedings of the American Mathematical Society, vol. 131 (2003), pp. 1971–1975.
[12]M., Foreman,M., Magidor, and S., Shelah, Martin's maximum, saturated ideals and nonregular ultrafilters, I, Annals of Mathematics, vol. 127 (1988), pp. 1–47.Google Scholar
[13] D.H., Fremlin, Notes on Farah P99, preprint, University of Essex, June 1999.
[14]F., Hausdorff, Die Graduierung nach dem Endverlauf, Abhandlungen der Königlich Sächsischen Gesellschaft derWissenschaften;Mathematisch–Physische Klasse, vol. 31 (1909), pp. 296–334.
[15]W., Just, Repercussions on a problem of Erdös and Ulam about density ideals, Canadian Journal of Mathematics, vol. 42 (1990), pp. 902–914.
[16] W., Just, A modification of Shelah's oracle chain condition with applications, Transactions of the American Mathematical Society, vol. 329 (1992), pp. 325–341.
[17] W., Just, A weak version of AT from OCA, Mathematical Science Research Institute Publications, vol. 26 (1992), pp. 281–291.
[18]W., Just and A., Krawczyk, On certain Boolean algebras P(ω)/I, Transactions of the American Mathematical Society, vol. 285 (1984), pp. 411–429.
[19]A., Kanamori, The higher infinite: large cardinals in set theory from their beginnings, Perspectives inMathematical Logic, Springer-Verlag, Berlin-Heidelberg-New York, 1995.
[20]V., Kanovei and M., Reeken, On Ulam's problem concerning the stability of approximate homomorphisms,TrudyMatematicheskogo Instituta Imeni V.A.Steklova. RossiıskayaAkademiya Nauk, vol. 231 (2000), no. Din. Sist., Avtom. i Beskon. Gruppy, pp. 249–283.
[21] V., Kanovei and M., Reeken, New Radon–Nikodym ideals,Mathematika, vol. 47 (2002), pp. 219–227.
[22]K., Kunen, К, λ-gaps under MA, preprint, 1976.
[23]C., Laflamme, Combinatorial aspects of F filters with an application to N-sets,Proceedings of the American Mathematical Society, vol. 125 (1997), pp. 3019–3025.
[24]A., Louveau and B., Velickovic, A note on Borel equivalence relations,Proceedings of the American Mathematical Society, vol. 120 (1994), pp. 255–259.
[25]B., Löwe and J., Steel, An introduction to core model theory,Sets and proofs, Logic Colloquium 1997, volume 1, London Mathematical Society Lecture Note Series, no. 258, Cambridge University Press, 1999.
[26]K., Mazur, F -ideals and 11 -gaps in the Boolean algebra P/I, Fundamenta Mathematicae, vol. 138 (1991), pp. 103–111.
[27]W., Rudin, Homogeneity problems in the theory of čech compactifications,Duke Mathematics Journal, vol. 23 (1956), pp. 409–419.
[28]S., Shelah, Proper forcing, Lecture Notes inMathematics 940, Springer, 1982.
[29]S., Shelah and J., Steprāns, PFA implies all automorphisms are trivial,Proceedings of the American Mathematical Society, vol. 104 (1988), pp. 1220–1225.Google Scholar
[30] S., Shelah and J., Steprāns, Non-trivial homeomorphisms of βN\N without the continuum hypothesis, Fundamenta Mathematicae, vol. 132 (1989), pp. 135–141.Google Scholar
[31]S., Shelah and W., H. Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable,Israel Journal of Mathematics, vol. 70 (1990), pp. 381–394.
[32]S., Solecki, Analytic ideals,The Bulletin of Symbolic Logic, vol. 2 (1996), pp. 339–348.Google Scholar
[33] S., Solecki, Analytic ideals and their applications,Annals of Pure and Applied Logic, vol. 99 (1999), pp. 51–72.Google Scholar
[34] S., Solecki, Filters and sequences,Fundamenta Mathematicae, vol. 163 (2000), pp. 215–228.Google Scholar
[35]R., Solovay, A model of set theory in which every set of reals is Lebesgue measurable,Annals of Mathematics, vol. 92 (1970), pp. 1–56.Google Scholar
[36]S., Todorčević, Partition problems in topology, Contemporary Mathematics, vol. 84, American Mathematical Society, Providence, Rhode Island, 1989.
[37] S., Todorčević, Definable ideals and gaps in their quotients,Set theory: Techniques and applications (C., A. et al., editors), Kluwer Academic Press, 1997, pp. 213–226.
[38] S., Todorčević, Basis problems in combinatorial set theory,Proceedings of the international congress of mathematicians, vol. II (Berlin, 1998), DocumentaMathematica, 1998, pp. 43–52.
[39] S., Todorčević, Gaps in analytic quotients,Fundamenta Mathematicae, vol. 156 (1998), pp. 85–97.Google Scholar
[40] B., Velickovic, Definable automorphisms of P/Fin, Proceedings of the American Mathematical Society, vol. 96 (1986), pp. 130–135.Google Scholar
[41] B., Velickovic, OCA and automorphisms of P/Fin, Topology and its Applications, vol. 49 (1992), pp. 1–12.Google Scholar
[42]W., Weiss, Partitioning topological spaces,Mathematics of Ramsey Theory (J., Nešetřil and V., Rödl, editors), Algorithms and Combinatorics, vol. 5, Springer-Verlag, Berlin, 1990, pp. 154–171.
[43] W.H., Woodin, Σ21 Σabsoluteness, handwritten note of May 1985.
[44] W.H., Woodin, The axiom of determinacy, forcing axioms and the nonstationary ideal, deGruyter Series in Logic and Its Applications, vol. 1, de Gruyter, 1999Google 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
×