Publications and Notes (H. Sakai)
Publications
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(with S. Cox)
Martin's Maximum and the Diagonal Reflection Principle
Submitted to RIMS Kokyuroku.
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(with S. Fuchino and A.O.M. Rodorigues)
Strong downward Lowenheim-Skolem therorems for stationary logics, III
To appear in Proceedings of 16th Asian Logic Conference.
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(with S. Fuchino and A.O.M. Rodorigues)
Strong downward Lowenheim-Skolem therorems for stationary logics, II
To appear in Archive for Mathematical Logic.
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(with S. Fuchino and A.O.M. Rodorigues)
Strong downward Lowenheim-Skolem therorems for stationary logics, I
To appear in Archive for Mathematical Logic.
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(with B. Cody)
How much weak compactness does the weakly compact reflection principle imply?
Archive for Mathematical Logic 59 (2020), no.1, 179--196.
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(with S. Cox)
A variant of Shelah's characterization of Strong Chang's Conjecture
Mathematical Logic Quarterly 65 (2019), no.2, 251--257.
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(with Y. Matsubara and T. Usuba)
On the existence of skinny stationary subsets
Annals of Pure and Applied Logic 170 (2019), no.5, 539--557.
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On Katetov and Katetov-Blass orders on analytic P-ideals and Borel ideals
Archive for Mathematical Logic 57 (2018), no.3--4, 317--327.
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(with H. Minami)
Katetov and Katetov-Blass orders on F_\sigma-ideals
Archive for Mathematical Logic 55 (2016), no.7, 883--898.
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Separation of MA^+ (sigma-closed) from stationary reflection principles
submitted.
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(with J. Bagaria and M. Magidor)
Reflection and indescribability in the constructible universe
Israel Journal of Mathematics 208 (2015), pp.1--11.
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Simple proofs of SCH from reflection principles without using better scales
Archive for Mathematical Logic 54 (2015), no.5, pp.639--647.
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Note on covering and approximation properties
RIMS Kokyuroku no.1949, pp.81-88, 2015.
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(with B. Velickovic)
Stationary reflection principles and two cardinal tree properties
Journal of the Institute of Mathematics of Jussieu 14 (2015), no.1, pp.69--85.
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Chang's conjecture and weak square
Archive for Mathematical Logic 52 (2013), no.1-2, pp.29--45.
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(with M. Kikuchi and T. Kurahashi)
On proofs of the incompleteness theorems based on Berry's paradox
by Vopenka, Chaitin, and Boolos
Mathematical Logic Quarterly 58 (2012), no.4-5, pp.307--316.
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Partial square at omega_1 is implied by MM but not by PFA
Fundamenta Mathematicae 215 (2011), pp.109--131.
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On standard model of Martin's Maximum
RIMS Kokyuroku no.1754, pp.97-107, 2011.
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On preservation and reflection of stationary subsets
of P_\kappa \lambda when cof( \lambda ) < \kappa
the Proceedings of the 10th Asian Logic Conference,
pp.271--299, World Sci. Publ., 2010.
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Partial stationary reflection in P_{\omega_1} \omega_2
RIMS Kokyuroku no.1595, pp.47-62, 2008.
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Semistationary and stationary reflection
Journal of Symbolic Logic 73 (2008), no.1, pp.181-192.
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(with S. Fuchino, M. Karato and T. Usuba)
\kappa^\kappa in light of Tukey ordering
RIMS Kokyuroku no.1471, pp.19-34, 2006.
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Semiproper ideals
Fundamenta Mathematicae 186 (2005), no.3, pp.251-267.
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Generalized Prikry forcing and iteration of generic ultrapowers
Mathematical Logic Quarterly 51, no.5, pp.507-523, 2005.
Notes
Hiroshi Sakai
Graduate School of System Informatics
Kobe University
E-mail: