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Published online by Cambridge University Press:  10 November 2022

John R. Steel
John R. Steel
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University of California, Berkeley
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A Comparison Process for Mouse Pairs , pp. 527 - 532
Publisher: Cambridge University Press
Print publication year: 2022

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References

Andretta, Alessandro, Neeman, Itay, and Steel, John, The domestic levels of Kc are iterable, Israel Journal of Mathematics, vol. 125 (2001), pp. 157–201.Google Scholar
Baldwin, Stewart, Generalizing the Mahlo hierarchy, with applications to the Mitchell models, Annals of Pure and Applied Logic, vol. 25 (1983), pp. 103–127.Google Scholar
Baldwin, Stewart, Between strong and superstrong, The Journal of Symbolic Logic, vol. 51 (1986), pp. 547–559.Google Scholar
Dodd, Anthony J., Strong cardinals, Unpublished notes, circa 1982.Google Scholar
Dodd, Anthony J. and Jensen, Ronald B., The core model, Annals of Mathematical Logic, vol. 20 (1981), pp. 43–75.Google Scholar
Dodd, Anthony J. and Jensen, Ronald B., The covering lemma for K, Annals of Mathematical Logic, vol. 22 (1982), pp. 1–30.Google Scholar
Dodd, Anthony J. and Jensen, Ronald B., The covering lemma for LU, Annals of Mathematical Logic, vol. 22 (1982), pp. 127–155.CrossRefGoogle Scholar
Farah, Ilijas, The extender algebra and Σ21 absoluteness, Large Cardinals, Determinacy, and Other Topics. The Cabal Seminar, Volume IV (Kechris, A. S. et al., editors), Lecture Notes in Logic, vol. 43, Association for Symbolic Logic, Ithaca, New York, 2020, pp. 155–192.Google Scholar
Feng, Qi, Magidor, Menachem, and Woodin, W. Hugh, Universally Baire sets of reals, Set Theory of the Continuum (Berkeley, CA, 1989) (New York), Mathematical Sciences Research Institute Publications, vol. 26, Springer, 1992, pp. 208–242.Google Scholar
Fuchs, Gunter, λ-structures and s-structures: translating the iteration strategies, Annals of Pure and Applied Logic, vol. 162 (2011), pp. 710–751.Google Scholar
Fuchs, Gunter, λ-structures and s-structures: translating the models, Annals of Pure and Applied Logic, vol. 162 (2011), pp. 257–317.Google Scholar
Fuchs, Gunter, Hamkins, Joel, and Rietz, Jonas, Set-theoretic geology, Annals of Pure and Applied Logic, vol. 166 (2015), pp. 464–501.Google Scholar
Fuchs, Gunter, Neeman, Itay, and Schindler, Ralf, A criterion for coarse iterability, Archive for Mathematical Logic, vol. 49 (2010), pp. 447–467.Google Scholar
GöDEL, Kurt F., The Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis with the Axioms of Set Theory, Annals of Mathematical Studies, vol. 3, Princeton University Press, Princeton, New Jersey, 1940.Google Scholar
Harrington, Leo A. and Kechris, Alexander S., On the determinacy of games on ordinals, Annals of Mathematical Logic, vol. 20 (1981), pp. 109–154.Google Scholar
Hjorth, Gregory, A boundedness lemma for iterations, The Journal of Symbolic Logic, vol. 66 (2001), pp. 1058–1072.Google Scholar
Jackson, Stephen, Sargsyan, Grigor, and Steel, John, Suslin cardinals and cutpoints in mouse limits, https://arxiv.org/abs/2207.04042, (2022).Google Scholar
Jensen, Ronald B., The fine structure of the constructible hierarchy, Annals of Mathematical Logic, vol. 4 (1972), pp. 229–308.Google Scholar
Jensen, Ronald B., A new fine structure for higher core models, (1997), manuscript available at https://www.mathematik.hu-berlin.de/∼raesch/org/jensen.html.Google Scholar
Jensen, Ronald B., Addendum to “A new fine structure for higher core models”, (1998), manuscript available at https://www.mathematik.hu-berlin.de/∼raesch/org/jensen.html.Google Scholar
Jensen, Ronald B., Smooth iterations, (2018), preprint available at https://www.mathematik.hu-berlin.de/∼raesch/org/jensen.html.Google Scholar
Jensen, Ronald B. and Steel, John R., K without the measurable, The Journal of Symbolic Logic, vol. 73 (2013), pp. 708–733.Google Scholar
Kechris, Alexander S., Countable ordinals and the analytical hierarchy, Pacific Journal of Mathematics, vol. 60 (1975), pp. 223–227.Google Scholar
Kechris, Alexander S., The theory of countable analytical sets, Transactions of the American Mathematical Society, vol. 202 (1975), pp. 259–297.Google Scholar
Ketchersid, Richard, Toward ADℝ from the Continuum Hypothesis and an ω1-dense ideal, Ph.D. thesis, Berkeley, 2000.Google Scholar
Koellner, Peter and Hugh Woodin, W., Large cardinals from determinacy, Handbook of Set Theory, Vol. 3 (Foreman, M. and Kanamori, A., editors), Springer-Verlag, 2010, pp. 1951–2120.Google Scholar
Kunen, Kenneth, Some applications of iterated ultrapowers in set theory, Annals of Mathematical Logic, vol. 1 (1970), pp. 179–227.Google Scholar
Larson, Paul, The Stationary Tower: Notes on a Course by Hugh Woodin, University Lecture Series, vol. 32, American Mathematical Society, Providence, RI, 2004.Google Scholar
Martin, Donald A. and Steel, John R., A proof of projective determinacy, Journal of the American Mathematical Society, vol. 2 (1989), pp. 71–126.Google Scholar
Martin, Donald A. and Steel, John R., Iteration trees, Journal of the American Mathematical Society, vol. 7 (1994), pp. 1–73.Google Scholar
Mitchell, William J., Sets constructible from sequences of ultrafilters, The Journal of Symbolic Logic, vol. 39 (1974), pp. 57–66.Google Scholar
Mitchell, William J., Hypermeasurable cardinals, Logic Colloquium ’78 (Mons 1978) (Amsterdam – New York) (Boffa, M. et al., editors), Studies in Logic and the Foundations of Mathematics, North Holland, 1979, pp. 303–316.Google Scholar
Mitchell, William J., Coherent sequences of measures: revisited, The Journal of Symbolic Logic, vol. 48 (1983), pp. 600–609.Google Scholar
Mitchell, William J. and Schindler, Ralf D., A universal extender model without large cardinals in V, The Journal of Symbolic Logic, vol. 69 (2004), pp. 371–386.Google Scholar
Mitchell, William J. and Steel, John R., Fine Structure and Iteration Trees, Lecture Notes in Logic, vol. 3, Springer-Verlag, Berlin, 1994.Google Scholar
Myhill, John and Scott, Dana, Ordinal definability, Axiomatic Set Theory, Proceedings of Symposia in Pure Mathematics, Vol. XIII, Part I, UCLA, (1967) (Providence, R.I.), American Mathematical Society, 1971, pp. 271–278.Google Scholar
Neeman, Itay, Inner models in the region of a Woodin limit of Woodin cardinals, Annals of Pure and Applied Logic, vol. 116 (2002), pp. 67–155.Google Scholar
Neeman, Itay, Determinacy in L(ℝ), Handbook of Set Theory, Vols. 1, 2, 3 (Foreman, M. and Kanamori, A., editors), Springer, Dordrecht, 2010, pp. 1877–1950.Google Scholar
Neeman, Itay and John, Steel, A weak Dodd-Jensen lemma, The Journal of Symbolic Logic, vol. 64 (1999), pp. 1285–1294.Google Scholar
Neeman, Itay and John, Steel, Counterexamples to the unique and cofinal branches hypotheses, The Journal of Symbolic Logic, vol. 71 (2006), pp. 977–988.Google Scholar
Neeman, Itay and John, Steel, Equiconsistencies at subcompact cardinals, Archive for Mathematical Logic, vol. 55 (2016), pp. 207–238.Google Scholar
Sargsyan, Grigor, A Tale of Hybrid Mice, Ph.D. thesis, UC Berkeley, Ann Arbor, MI, 2009.Google Scholar
Sargsyan, Grigor, Hod Mice and the Mouse Set Conjecture, Memoirs of the American Mathematical Society, vol. 236, American Mathematical Society, Providence, RI, 2015.Google Scholar
Sargsyan, Grigor and Trang, Nam, The largest Suslin axiom, (2016), preprint.Google Scholar
Schilling, Kenneth, On absolutely Δ12 operations, Fundamenta Mathematicae, vol. 121 (1984), pp. 239–250.Google Scholar
Schimmerling, Ernest, Woodin cardinals, Shelah cardinals, and the Mitchell-Steel core model, Proceedings of the American Mathematical Society, vol. 130 (2002), pp. 3385–3391.Google Scholar
Schimmerling, Ernest and John, Steel, Fine structure for tame inner models, The Journal of Symbolic Logic, vol. 61 (1996), pp. 621–639.Google Scholar
Schimmerling, Ernest and John, Steel, The maximality of the core model, Transactions of the American Mathematical Society, vol. 351 (1999), pp. 3119–3141.Google Scholar
Schimmerling, Ernest and Martin, Zeman, Characterization of ☐κ in core models, Journal of Mathematical Logic, vol. 4 (2004), pp. 1–72.Google Scholar
Schindler, Ralf, Core models in the presence of Woodin cardinals, The Journal of Symbolic Logic, vol. 71 (2006), pp. 1145–1154.Google Scholar
Schindler, Ralf and John, Steel, The self-iterability of L[Ē], The Journal of Symbolic Logic, vol. 74 (2009), pp. 751–779.Google Scholar
Schindler, Ralf and John, Steel, The Core Model Induction, 2014, preliminary draft available at www.math.uni-muenster.de/logik/Personen/rds.Google Scholar
Schindler, Ralf, Steel, John, and Zeman, Martin, Deconstructing inner model theory, The Journal of Symbolic Logic, vol. 67 (2002), pp. 721–736.Google Scholar
Schindler, Ralf and Martin, Zeman, Fine structure, Handbook of Set Theory, Vols. 1, 2, 3 (Foreman, M. and Kanamori, A., editors), Springer, Dordrecht, 2010, pp. 605–656.Google Scholar
Schlutzenberg, Farmer, Measures in Mice, Ph.D. thesis, Berkeley, 2007.Google Scholar
Schlutzenberg, Farmer, Reconstructing copying and condensation, (2015), preprint available at https://sites.google.com/site/schlutzenberg/home.Google Scholar
Schlutzenberg, Farmer, Iterability for (transfinite) stacks, Journal of Mathematical Logic, vol. 21 (2021).Google Scholar
Schlutzenberg, Farmer, Definability of E in self-iterable mice, (March 2019), preprint available at https://sites.google.com/site/schlutzenberg/home.Google Scholar
Schlutzenberg, Farmer, Fine structure from normal iterability, (November 2019), preprint at arXiv:2011.10037v2 [math.LO].Google Scholar
Schlutzenberg, Farmer and John, Steel, Comparison of fine structural mice by coarse iteration, Archive for Mathematical Logic, vol. 53 (2014), pp. 539–559.Google Scholar
Schlutzenberg, Farmer and Nam, Trang, Scales in hybrid mice over ℝ, (2016), preprint available at https://sites.google.com/site/schlutzenberg/home.Google Scholar
Silver, Jack, Measurable cardinals and Δ13 well orderings, Annals of Mathematics, vol. 94 (1971), pp. 414–446.Google Scholar
Siskind, Benjamin, Aspects of Martin’s Conjecture and Inner Model Theory, Ph.D. thesis, Berkeley, 2021.Google Scholar
Siskind, Benjamin and John, Steel, Full normalization for mouse pairs, https://arxiv.org/abs/2207.11065, (2022).Google Scholar
Steel, John R., HODL(ℝ) is a core model below θ, The Bulletin of Symbolic Logic, vol. 1 (1995), pp. 75–84.CrossRefGoogle Scholar
Steel, John R., The Core Model Iterability Problem, Lecture Notes in Logic, vol. 8, Springer-Verlag, Berlin, 1996.Google Scholar
Steel, John R., Local Kc constructions, The Journal of Symbolic Logic, vol. 72 (2007), pp. 721–737.Google Scholar
Steel, John R., Derived models associated to mice, Computational Prospects of Infinity. Part I. Tutorials, Lecture Notes Series, Institute of Mathematical Sciences, National University of Singapore, vol. 14, World Scientific Publishers, Hackensack, NJ, 2008, pp. 105–193.Google Scholar
Steel, John R., The derived model theorem, Logic Colloquium 2006 (Cooper et al., editors), Lecture Notes in Logic, vol. 32, Association for Symbolic Logic, Chicago, IL, 2009, pp. 280–327.Google Scholar
Steel, John R., An outline of inner model theory, Handbook of Set Theory, Vols. 1, 2, 3 (Foreman, M. and Kanamori, A., editors), Springer, Dordrecht, 2010, pp. 580–645.Google Scholar
Steel, John R., A theorem of Woodin on mouse sets, Ordinal Definability and Recursion Theory. The Cabal Seminar, Volume III (Kechris, A. S. et al., editors), Lecture Notes in Logic, vol. 43, Association for Symbolic Logic, Ithaca, New York, 2016, pp. 243–256.Google Scholar
Steel, John R., HOD in models of determinacy, Ordinal Definability and Recursion Theory. The Cabal Seminar, Volume III (Kechris, A. S. et al., editors), Lecture Notes in Logic, vol. 43, Association for Symbolic Logic, Ithaca, New York, 2016, pp. 3–48.Google Scholar
Steel, John R., Mouse pairs and Suslin cardinals, Proceedings of the 2019 workshop “Higher Recursion Theory and Set Theory” (Chong, C. T. et. al., editor), Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, World Scientific Publishing Co., 2022.Google Scholar
Steel, John R., The comparison lemma, (2022), preprint available at www.math.berkeley.edu/∼steel.Google Scholar
Steel, John R., Remarks on a paper by Sargsyan, (April 2013), notes available at www.math.berkeley.edu/∼steel.Google Scholar
Steel, John R., Remarks on a hod mouse construction, (August 2014), notes available at www.math.berkeley.edu/∼steel.Google Scholar
Steel, John R., Local HOD computation, (July 2016), notes available at www. math.berkeley.edu/∼steel.Google Scholar
Steel, John R., LSA from least branch hod pairs, (July 2016), notes available at www.math.berkeley.edu/∼steel.Google Scholar
Steel, John R., Hod mice below LST−, (October 2013), notes available at www. math.berkeley.edu/∼steel.Google Scholar
Steel, John R., Hod pair capturing and short tree strategies, (October 2016), notes available at www.math.berkeley.edu/∼steel.Google Scholar
Steel, John R. and Nam, Trang, Condensation for mouse pairs, https://arxiv.org/abs/2207.03559, (2022).Google Scholar
Steel, John R. and Hugh Woodin, W., HOD as a core model, Ordinal Definability and Recursion Theory. The Cabal Seminar, Volume III (Kechris, A. S. et al., editors), Lecture Notes in Logic, vol. 43, Association for Symbolic Logic, Ithaca, New York, 2016, pp. 257–348.Google Scholar
Welch, Philip D., Σ∗ fine structure, Handbook of Set Theory, Vols. 1, 2, 3 (Foreman, M. and Kanamori, A., editors), Springer, Dordrecht, 2010, pp. 657–736.Google Scholar
woodin, W. Hugh, Suitable extender models I, Journal of Mathematical Logic, vol. 10 (2010), pp. 101–339.Google Scholar
woodin, W. Hugh, In search of Ultimate L: the 19th Midrasha Mathematicae lectures, The Bulletin of Symbolic Logic, vol. 23 (2017), pp. 1–109.Google Scholar
Zeman, Martin, Inner Models and Large Cardinals, De Gruyter Series in Logic and its Applications, vol. 5, Walter De Gruyter, Berlin, 2001.Google Scholar
Zeman, Martin, Dodd parameters and the λ-indexing of extenders, Journal of Mathematical Logic, vol. 04 (2004), pp. 73–108.Google Scholar

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  • References
  • John R. Steel, University of California, Berkeley
  • Book: A Comparison Process for Mouse Pairs
  • Online publication: 10 November 2022
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  • References
  • John R. Steel, University of California, Berkeley
  • Book: A Comparison Process for Mouse Pairs
  • Online publication: 10 November 2022
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  • References
  • John R. Steel, University of California, Berkeley
  • Book: A Comparison Process for Mouse Pairs
  • Online publication: 10 November 2022
Available formats
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