Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-26T13:27:48.226Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  aN Invalid Date NaN

Grigor Sargsyan  and
Nam Trang
Grigor Sargsyan
Affiliation:
Polish Academy of Sciences
Nam Trang
Affiliation:
University of North Texas
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
The Largest Suslin Axiom , pp. 385 - 390
Publisher: Cambridge University Press
Print publication year: 2024

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

Adolf, Dominik and Sargsyan, Grigor, Derived models of mice below the least fixpoint of the Solovay sequence, The Journal of Symbolic Logic, vol. 84 (2019), no. 1, pp. 27–53.CrossRefGoogle Scholar
Adolf, Dominik, Sargsyan, Grigor, Trang, Nam, Wilson, Trevor, and Zeman, Martin, Ideals and strong axioms of determinacy, available at https://arxiv.org/abs/2111.06220, 2021.Google Scholar
Andretta, Alessandro, Neeman, Itay, and Steel, John, The domestic levels of Kc are iterable, Israel Journal of Mathematics, vol. 125 (2001), pp. 157–201.CrossRefGoogle Scholar
s Eduardo Caicedo, André, Larson, Paul, Sargsyan, Grigor, Schindler, Ralf, Steel, John, and Zeman, Martin, Square principles in ℙmax extensions, Israel Journal of Mathematics, vol. 217 (2017), pp. 231–261.CrossRefGoogle Scholar
Cramer, Scott, Implications of very large cardinals, Essays in honor of W. Hugh Woodin’s 60th birthday. Proceedings of the Logic at Harvard Conference held at Harvard University, Cambridge, MA, March 27–29, 2015 (Caicedo, A. E., Cummings, J., Koellner, P., and Larson, P. B., editors), American Mathematical Society, Providence, RI, 2017, pp. 225–257.Google Scholar
KeithDevlin, J, Constructibility, Springer, 1984.Google Scholar
Farah, Ilijas, The extender algebra and Σ12 absoluteness, Large Cardinals, Determinacy, and Other Topics. The Cabal Seminar, Volume IV (Kechris, A. S., Löwe, B., and Steel, J. R., editors), Lecture Notes in Logic, vol. 43, Cambridge University Press and Association for Symbolic Logic, 2020, pp. 155–192.Google Scholar
Fuchs, Gunter, λ-structures and s-structures: translating the iteration strategies, Annals of Pure and Applied Logic, vol. 162 (2011), no. 9, pp. 710–751.CrossRefGoogle Scholar
Fuchs, Gunter, λ-structures and s-structures: translating the models, Annals of Pure and Applied Logic, vol. 162 (2011), no. 4, pp. 257–317.CrossRefGoogle Scholar
Jensen, Ronald, The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308; erratum, ibid. 4 (1972), 443, with a section by Jack Silver.CrossRefGoogle Scholar
Jensen, Ronald, Manuscript on fine structure, inner model theory, and the core model below one Woodin cardinal, available at https://www.mathematik.hu-berlin.de/~raesch/org/jensen.html, 2020.Google Scholar
Jensen, Ronald, Schimmerling, Ernest, Schindler, Ralf, and Steel, John, Stacking mice, The Journal of Symbolic Logic, vol. 74 (2009), no. 1, pp. 315–335.CrossRefGoogle Scholar
Kechris, Alexander S., Kleinberg, Eugene M., Moschovakis, Yiannis N., and Hugh Woodin, W., The axiom of determinacy, strong partition properties and nonsingular measures, Cabal Seminar 77 – 79. Proceedings Caltech-UCLA Logic Seminar, 1977–79), Lecture Notes in Mathematics, vol. 839, Springer, Berlin, 1981, pp. 75–99.Google Scholar
Kechris, Alexander S., Löwe, Benedikt, and Steel, John R., Games, Scales and Suslin Cardinals – The Cabal Seminar, Volume I, Lecture Notes in Logic, vol. 31, Cambridge University Press and Association for Symbolic Logic, 2008.CrossRefGoogle Scholar
Kechris, Alexander S., Löwe, Benedikt, and Steel, John R., Wadge Degrees and Projecive Ordinals – The Cabal Seminar, Volume II, Lecture Notes in Logic, vol. 37, Cambridge University Press and Association for Symbolic Logic, 2012.Google Scholar
Kechris, Alexander S., Löwe, Benedikt, and Steel, John R., Ordinal Definability and Recursion Theory – The Cabal Seminar, Volume III, Lecture Notes in Logic, vol. 43, Cambridge University Press and Association for Symbolic Logic, 2016.CrossRefGoogle Scholar
Kechris, Alexander S., Löwe, Benedikt, and Steel, John R., Large Cardinals, Determinacy and Other Topics – The Cabal Seminar, Volume IV, Lecture Notes in Logic, vol. 49, Cambridge University Press and Association for Symbolic Logic, 2021.Google Scholar
Koellner, Peter and Hugh Woodin, W., Large cardinals from determinacy, Handbook of Set Theory. Vols. 1, 2, 3, Springer, Dordrecht, 2010, pp. 1951–2119.CrossRefGoogle Scholar
Larson, Paul B., The Stationary Tower: Notes on a Course by W. Hugh Woodin, University Lecture Series, vol. 32, American Mathematical Society, Providence, RI, 2004.Google Scholar
Larson, Paul B., An introduction to AD+, unpublished, available at https://paulblarson.github.io/, 2022.Google Scholar
Larson, Paul B. and Sargsyan, Grigor, Failures of square in Pmax extensions of Chang models, available at https://arxiv.org/abs/2105.00322, 2021.Google Scholar
Martin, Donald A. and Steel, John R., Iteration trees, Journal of the American Mathematical Society, vol. 7 (1994), no. 1, pp. 1–73.CrossRefGoogle Scholar
Mitchell, William J. and Steel, John R., Fine Structure and Iteration Trees, Lecture Notes in Logic, vol. 3, Springer-Verlag, Berlin, 1994.CrossRefGoogle Scholar
Moschovakis, Yiannis N., Descriptive Set Theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland, Amsterdam, 1980.Google Scholar
Neeman, Itay, Optimal proofs of determinacy, The Bulletin of Symbolic Logic, vol. 1 (1995), no. 3, pp. 327–339.CrossRefGoogle Scholar
Neeman, Itay, Inner models in the region of a Woodin limit of Woodin cardinals, Annals of Pure and Applied Logic, vol. 116 (2002), no. 1-3, pp. 67–155.CrossRefGoogle Scholar
Neeman, Itay and Steel, John, Equiconsistencies at subcompact cardinals, Archive for Mathematical Logic, vol. 55 (2016), no. 1-2, pp. 207–238.CrossRefGoogle Scholar
Sargsyan, Grigor, Descriptive inner model theory, The Bulletin of Symbolic Logic, vol. 19 (2013), no. 1, pp. 1–55.CrossRefGoogle Scholar
Sargsyan, Grigor, Hod Mice and the Mouse Set Conjecture, vol. 236, Memoirs of the American Mathematical Society, no. 1111, American Mathematical Society, 2014.Google Scholar
Sargsyan, Grigor, Nontame mouse from the failure of square at a singular strong limit cardinal, Journal of Mathematical Logic, vol. 14 (2014), no. 01, p. 1450003.CrossRefGoogle Scholar
Sargsyan, Grigor, Covering with universally Baire operators, Advances in Mathematics, vol. 268 (2015), pp. 603–665.CrossRefGoogle Scholar
Sargsyan, Grigor, ADℝ implies that all sets of reals are Θ universally Baire, Archive for Mathematical Logic, vol. 60 (2021), no. 1-2, pp. 1–15.CrossRefGoogle Scholar
Sargsyan, Grigor, Negative results on precipitous ideals on ω1, The Journal of Symbolic Logic, vol. 88 (2023), pp. 490–509.CrossRefGoogle Scholar
Sargsyan, Grigor and Steel, John, The mouse set conjecture for sets of reals, The Journal of Symbolic Logic, vol. 80 (2015), no. 2, pp. 671–683.CrossRefGoogle Scholar
Sargsyan, Grigor and Trang, Nam, Non-tame mice from tame failures of the unique branch hypothesis, Canadian Journal of Mathematics, vol. 66 (2014), no. 4, pp. 903–923.CrossRefGoogle Scholar
Sargsyan, Grigor and Trang, Nam, The exact strength of generic absoluteness for the universally Baire sets, available at arxiv.org/abs/2110.02725, 2021.Google Scholar
Schimmerling, Ernest, Coherent sequences and threads, Advances in Mathematics, vol. 216 (2007), no. 1, pp. 89–117.CrossRefGoogle Scholar
Schimmerling, Ernest and Zeman, Martin, Characterization of □κ in core models, Journal of Mathematical Logic, vol. 4 (2004), no. 01, pp. 1–72.CrossRefGoogle Scholar
Schindler, Ralf and Steel, John R., The self-iterability of L[E], The Journal of Symbolic Logic, vol. 74 (2009), no. 3, pp. 751–779.CrossRefGoogle Scholar
Schindler, Ralf and Steel, John R., The core model induction, available at math.berkeley.edu/~steel, 2014.Google Scholar
Schindler, Ralf and Zeman, Martin, Fine structure, Handbook of Set Theory. Vols. 1, 2, 3, Springer, Dordrecht, 2010, pp. 605–656.CrossRefGoogle Scholar
Schindler, Ralf-Dieter, Steel, John, and Zeman, Martin, Deconstructing inner model theory, The Journal of Symbolic Logic, vol. 67 (2002), no. 2, pp. 721–736.CrossRefGoogle Scholar
Schindler, Ralf-Dieter, Steel, John, and Zeman, Martin, Deconstructing inner model theory, The Journal of Symbolic Logic, vol. 67 (2002), no. 2, pp. 721–736.CrossRefGoogle Scholar
Schlutzenberg, Farmer, Measures in Mice, ProQuest LLC, Ann Arbor, MI, 2007, Ph.D. thesis, University of California, Berkeley.Google Scholar
Schlutzenberg, Farmer, Reconstructing resurrection, to appear, available at https://arxiv. org/abs/1811.04236, 2018.Google Scholar
Schlutzenberg, Farmer, A premouse inheriting strong cardinals from V, Annals of Pure and Applied Logic, vol. 171 (2020), no. 9, p. 66, Id/No 102826.CrossRefGoogle Scholar
Schlutzenberg, Farmer, Background construction for λ-indexed mice, available at https://arxiv.org/abs/2101.00889, 2021.Google Scholar
Schlutzenberg, Farmer, The definability of 𝔼 in self-iterable mice, Annals of Pure and Applied Logic, vol. 174 (2023), no. 2, p. 59, Id/No 103208.CrossRefGoogle Scholar
Schlutzenberg, Farmer and Steel, John R., Comparison of fine structural mice via coarse iteration, Archive for Mathematical Logic, vol. 53 (2014), no. 5-6, pp. 539–559.CrossRefGoogle Scholar
Schlutzenberg, Farmer and Trang, Nam, Scales in hybrid mice over ℝ, available at https://arxiv.org/abs/1210.7258, 2014.Google Scholar
Solovay, Robert M., Strongly compact cardinals and the GCH, Proceedings of the Tarski Symposium. An international symposium held to honor Alfred Tarski on the occasion of his seventieth birthday (Henkin, L., Addison, J., Chang, C. C., Craig, W., Scott, D., and Vaught, R., editors), Proceedings of Symposia in Pure Mathematics, vol. 25, American Mathematical Society, Providence, RI, 1974, pp. 365–372.Google Scholar
Steel, John R., The Core Model Iterability Problem, Lecture Notes in Logic, vol. 8, Springer-Verlag, Berlin, 1996.CrossRefGoogle Scholar
Steel, John R., Core models with more Woodin cardinals, The Journal of Symbolic Logic, vol. 67 (2002), no. 3, pp. 1197–1226.CrossRefGoogle Scholar
Steel, John R., A theorem of Woodin on mouse sets, unpublished notes, available at http://math.berkeley.edu/~steel/, 2004.Google Scholar
Steel, John R., PFA implies ADL(ℝ), The Journal of Symbolic Logic, vol. 70 (2005), no. 4, pp. 1255–1296.CrossRefGoogle Scholar
John, R. Steel, , A stationary-tower-free proof of the derived model theorem, Advances in logic, Contemp. Math., vol. 425, Amer. Math. Soc., Providence, RI, 2007, pp. 1–8.Google Scholar
Steel, John R., Derived models associated to mice, Computational Prospects of Infinity. Part I. Tutorials (Chong, C., , Q. Feng, , , T. A. Slaman, , , W. H. Woodin, , and Yang, Y., editors), Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, vol. 14, World Scientific, 2008, pp. 105–193.CrossRefGoogle Scholar
Steel, John R., The derived model theorem, Logic Colloquium 2006 (, S. B. Cooper, , Geuvers, H., Pillay, A., and Väänänen, J., editors), Lecture Notes in Logic, vol. 32, Cambridge University Press and Association for Symbolic Logic, 2009, pp. 280–327.CrossRefGoogle Scholar
Steel, John R., An outline of inner model theory, Handbook of Set Theory. Vols. 1, 2, 3, Springer, Dordrecht, 2010, pp. 1595–1684.CrossRefGoogle Scholar
Steel, John R., Hod mice below LST−, part I, handwritten notes, available at https://math.berkeley.edu/~steel/, 2013.Google Scholar
Steel, John R., Remarks on a paper by Sargsyan, handwritten notes, available at ttps://math.berkeley.edu/~steel/papers/remarks.sargsyan.pdf, 2015.Google Scholar
Steel, John R., Mouse pairs and Suslin cardinals, to appear, available at https://math.berkeley.edu/~steel/, 2016.Google Scholar
Steel, John R., A Comparison Process for Mouse Pairs, Lecture Notes in Logic, vol. 51, Cambridge University Press, 2023.Google Scholar
Trang, Nam, Generalized Solovay Measures, the HOD Analysis, and the Core Model Induction, Ph.D. thesis, University of California, Berkeley, 2013.Google Scholar
Trang, Nam, PFA and guessing models, Israel Journal of Mathematics, vol. 215 (2016), no. 2, pp. 607–667.CrossRefGoogle Scholar
Viale, Matteo and Weiss, Christoph, On the consistency strength of the proper forcing axiom, Advances in Mathematics, vol. 228 (2011), no. 5, pp. 2672–2687.CrossRefGoogle Scholar
Wilson, Trevor M., The envelope of a pointclass under a local determinacy hypothesis, Annals of Pure and Applied Logic, vol. 166 (2015), no. 10, pp. 991–1018.CrossRefGoogle Scholar
Hugh Woodin, W., The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal, 2nd revised ed., Walter de Gruyter, Berlin, 2010.CrossRefGoogle Scholar
Hugh Woodin, W., In search of ultimate-L. The 19th Midrasha mathematicae lectures, The Bulletin of Symbolic Logic, vol. 23 (2017), no. 1, pp. 1–109.CrossRefGoogle Scholar
Zeman, Martin, Inner Models and Large Cardinals, de Gruyter Series in Logic and its Applications, vol. 5, Walter de Gruyter & Co., Berlin, 2002.CrossRefGoogle 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.

  • References
  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book: The Largest Suslin Axiom
  • Chapter DOI: https://doi.org/10.1017/9781009520683.013
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.

  • References
  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book: The Largest Suslin Axiom
  • Chapter DOI: https://doi.org/10.1017/9781009520683.013
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.

  • References
  • Grigor Sargsyan, Polish Academy of Sciences, Nam Trang, University of North Texas
  • Book: The Largest Suslin Axiom
  • Chapter DOI: https://doi.org/10.1017/9781009520683.013
Available formats
×