Skip to main content Accessibility help
×
Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-25T05:25:18.860Z Has data issue: false hasContentIssue false

HOD as a core model

from PART V - HOD AND ITS LOCAL VERSIONS

Published online by Cambridge University Press:  05 December 2015

John R. Steel
Affiliation:
University of California, Berkeley
W. Hugh Woodin
Affiliation:
University of California, Berkeley
Alexander S. Kechris
Affiliation:
California Institute of Technology
Benedikt Löwe
Affiliation:
Universiteit van Amsterdam
John R. Steel
Affiliation:
University of California, Berkeley
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
Ordinal Definability and Recursion Theory
The Cabal Seminar, Volume III
, pp. 257 - 346
Publisher: Cambridge University Press
Print publication year: 2016

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

[BMS84] James, Baumgartner, Donald A., Martin, and Saharon, ShelahAxiomatic set theory. Proceedings of the AMS-IMS-SIAM joint summer research conference held in Boulder, Colo., June 19–25, 1983, Contemporary Mathematics, vol. 31, Amer. Math. Soc., Providence, RI, 1984.Google Scholar
[BK84] Howard S., Becker and Alexander S., KechrisSets of ordinals constructible from trees and the third Victoria Delfino problem, in Baumgartner et al. [BMS84], pp. 13–29.
[Far] Ilijas, FarahThe extender algebra and Σ21 -absoluteness, to appear.
[Hjo01] Gregory, HjorthA boundedness lemma for iterations, The Journal of Symbolic Logic, vol. 66 (2001), no. 3, pp. 1058–1072.Google Scholar
[KF10] Akihiro, Kanamori and Matthew, ForemanHandbook of set theory, Springer, 2010.Google Scholar
[Kec75B] Alexander S., KechrisThe theory of countable analytical sets, Transactions of the American Mathematical Society, vol. 202 (1975), pp. 259–297.Google Scholar
[Kec84] Alexander S., KechrisThe axiom of determinancy implies dependent choices in L(ℝ), The Journal of Symbolic Logic, vol. 49 (1984), no. 1, pp. 161–173.Google Scholar
[Cabal I] Alexander S., Kechris, Benedikt, Löwe, and John R., SteelGames, scales, and Suslin cardinals: the Cabal seminar, volume I, Lecture Notes in Logic, vol. 31, Cambridge University Press, 2008.Google Scholar
[Cabal i] Alexander S., Kechris and Yiannis N., MoschovakisCabal seminar 76–77, Lecture Notes in Mathematics, no. 689, Berlin, Springer, 1978.Google Scholar
[KS85] Alexander S., Kechris and Robert M., SolovayOn the relative consistency strength of determinacy hypotheses, Transactions of the American Mathematical Society, vol. 290 (1985), no. 1, pp. 179–211.Google Scholar
[Ket11] Richard, KetchersidMore structural consequences of AD, Set theory and its applications, Contemporary Mathematics, vol. 533, American Mathematical Society, Providence, RI, 2011, pp. 71–105.Google Scholar
[KW10] Peter, Koellner and W. Hugh, WoodinLarge cardinals from determinacy, in Kanamori and Foreman [KF10], pp. 1951–2119.
[MaS94] Donald A., Martin and John R., SteelIteration trees, Journal of the American Mathematical Society, vol. 7 (1994), no. 1, pp. 1–73.Google Scholar
[MiS94] William J., Mitchell and John R., SteelFine structure and iteration trees, Lecture Notes in Logic, vol. 3, Springer-Verlag, Berlin, 1994.Google Scholar
[Mos09] Yiannis N., MoschovakisDescriptive set theory, second ed., Mathematical Surveys and Monographs, vol. 155, American Mathematical Society, 2009.Google Scholar
[Nee95] Itay, NeemanOptimal proofs of determinacy, The Bulletin of Symbolic Logic, vol. 1 (1995), no. 3, pp. 327–339.Google Scholar
[Nee10] Itay, NeemanDeterminacy inL(ℝ), in Kanamori and Foreman [KF10], pp. 1877–1950.
[Sar09] Grigor, SargsyanA tale of hybrid mice, Ph.D. thesis, University of California, Berkeley, 2009.Google Scholar
[Sar13] Grigor, SargsyanA tale of hybrid mice, preprint, 2013.
[SS] Grigor, Sargsyan and John R., SteelCapturing by ℝ-mice, to appear.
[SS09] Ralf, Schindler and John R., SteelThe self-iterability of L[E], The Journal of Symbolic Logic, vol. 74 (2009), no. 3, pp. 751–779.Google Scholar
[Sol78B] Robert M., SolovayThe independence of DC from AD, in Kechris and Moschovakis [Cabal i], pp. 171–184.
[Ste95A] John R., SteelHODL(ℝ) is a core model below Θ, The Bulletin of Symbolic Logic, vol. 1 (1995), no. 1, pp. 75–84.Google Scholar
[Ste96] John R., SteelThe core model iterability problem, Lecture Notes in Logic, no. 8, Springer-Verlag, Berlin, 1996.Google Scholar
[Ste05] John R., SteelPFA implies ADL(ℝ), The Journal of Symbolic Logic, vol. 70 (2005), no. 4, pp. 1255–1296.Google Scholar
[Ste08A] John R., SteelDerived models associated to mice, Computational prospects of infinity. Part I. Tutorials, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, vol. 14, World Scientific Publishing, 2008, pp. 105–193.Google Scholar
[Ste08C] John R., SteelScales in K(ℝ), in Kechris et al. [Cabal I], pp. 176–208.
[Ste09] John R., SteelThe derived model theorem, Logic Colloquium 2006, Lecture Notes in Logic, vol. 19, Association for Symbolic Logic, 2009, pp. 280–327.Google Scholar
[Ste10B] John R., SteelAn outline of inner model theory, in Kanamori and Foreman [KF10], pp. 1595–1684.
[Ste16A] John R., SteelOrdinal definability in models of determinacy. Introduction to Part V, 2016, this volume.
[Ste16B] John R., SteelA theorem of Woodin on mouse sets, 2016, this volume.
[ST10] John R., Steel and Nam, Trang AD+, derived models, and Σ1 reflection, Notes from the firstMünster conference on hod mice and the core model induction, available at http://math.berkeley.edu/~namtrang/AD+reflection.pdf, 2010.
[Tra12] Nam, TrangHODin natural models of AD+, preprint, available at http://arXiv.org/abs/1201. 6128v1, 2012.
[Zhu10] Yizheng, ZhuThe derived model theorem II, Notes on lectures given by H. Woodin at the first Münster conference on hod mice and the core model induction, available at http://graduate.math.nus.edu.sg/~g0700513/der.pdf, 2010.
[Zhu12] Yizheng, ZhuRealizing anAD+ model as a derived model of a premouse, Ph.D. thesis, National University of Singapore, 2012.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org 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
×