Hostname: page-component-745bb68f8f-g4j75 Total loading time: 0 Render date: 2025-01-12T21:20:16.613Z Has data issue: false hasContentIssue false
  • English
  • Français

Large cardinals and large dilators

Published online by Cambridge University Press:  12 March 2014

Andy Lewis
Andy Lewis*
Affiliation:
Mathematics Virginia Commonwealth University, Box #842014, Richmond, VA 23284-2019, USA. E-mail:amlewis@saturn.vcu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Applying Woodin's non-stationary tower notion of forcing, I prove that the existence of a supercompact cardinal κ in V and a Ramsey dilator in some small forcing extension V[G] implies the existence in V of a measurable dilator of size κ, measurable by κ-complete measures.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 4 , December 1998 , pp. 1496 - 1510
Copyright
Copyright © Association for Symbolic Logic 1998

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

REFERENCES

[1] Girard, Jean-Yves, Π2 1-logic, Part 1: dilators, Journal of Mathematical Logic, vol. 21 (1981), pp. 75–219.Google Scholar
[2] Girard, Jean-Yves and Normann, Dag, Set recursion and Π2 1-logic, Annals of Pure and Applied Logic, vol. 28 (1985), pp. 255–286.Google Scholar
[3] Girard, Jean-Yves and Ressayre, Jean Pierre, Elements de logique Π n 1 , Proceedings of Symposia in Pure Mathematics, vol. 42 (1985), pp. 389–445.Google Scholar
[4] Griffor, E. R., An application of Π2 1-logic to descriptive set theory.Google Scholar
[5] Kechris, Alexander S., Dilators and ptykes in descriptive set theory, unpublished.Google Scholar
[6] Kechris, Alexander S., Kleinberg, Eugene, Moschovakis, Yiannis N., and Woodin, W. Hugh, The axiom of determincay, strong partition properties and nonsingular measures, Cabal seminar 77–79, Lecture Notes in Mathematics, vol. 839, 1981, pp. 75–100.Google Scholar
[7] Kechris, Alexander S. and Woodin, W. H., A strong boundedness theorem for dilators, Annals of Pure and Applied Logic, vol. 52 (1991), pp. 93–97.Google Scholar
[8] Lewis, Andrew M., Large dilators and large cardinals, Ph.D. thesis , University of California, Berkeley, 1993.Google Scholar
[9] Martin, Donald A. and Steel, John R., A proof of projective determinacy, Journal of the American Mathematical Society, vol. 2 (1989), pp. 71–125.Google Scholar
[10] Moschovakis, Yiannis Nicholas, Descriptive set theory, North-Holland Publishing Company, New York, 1980.Google Scholar
[11] Ressayre, J. P., Π2 1-logic and uniformization in the analytical hierarchy, Archives of Mathematical Logic, vol. 28 (1989), pp. 99–117.Google Scholar
[12] de Wiele, Jacques Van, Recursive dilators and generalized recursion, Proceedings of the Hebron symposium, Logic colloquium '81, North-Holland Publishing Company, New York, 1982.Google Scholar
[13] Woodin, W. Hugh, Supercompact cardinals, sets of reals, and weakly homogeneous trees, Proceedings of the National Academy of Science, USA, vol. 85 (1988), pp. 6587–6591.Google Scholar