Publications and Notes (H. Sakai)

Publications

• (with S. Cox)
  Martin's Maximum and the Diagonal Reflection Principle
  Submitted to RIMS Kokyuroku.
• (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.
• (with S. Fuchino and A.O.M. Rodorigues)
  Strong downward Lowenheim-Skolem therorems for stationary logics, II
  To appear in Archive for Mathematical Logic.
• (with S. Fuchino and A.O.M. Rodorigues)
  Strong downward Lowenheim-Skolem therorems for stationary logics, I
  To appear in Archive for Mathematical Logic.
• (with B. Cody)
  How much weak compactness does the weakly compact reflection principle imply?
  Archive for Mathematical Logic 59 (2020), no.1, 179--196.
• (with S. Cox)
  A variant of Shelah's characterization of Strong Chang's Conjecture
  Mathematical Logic Quarterly 65 (2019), no.2, 251--257.
• (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.
• On Katetov and Katetov-Blass orders on analytic P-ideals and Borel ideals
  Archive for Mathematical Logic 57 (2018), no.3--4, 317--327.
• (with H. Minami)
  Katetov and Katetov-Blass orders on F_\sigma-ideals
  Archive for Mathematical Logic 55 (2016), no.7, 883--898.
• Separation of MA^+ (sigma-closed) from stationary reflection principles
  submitted.
• (with J. Bagaria and M. Magidor)
  Reflection and indescribability in the constructible universe
  Israel Journal of Mathematics 208 (2015), pp.1--11.
• Simple proofs of SCH from reflection principles without using better scales
  Archive for Mathematical Logic 54 (2015), no.5, pp.639--647.
• Note on covering and approximation properties
  RIMS Kokyuroku no.1949, pp.81-88, 2015.
• (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.
• Chang's conjecture and weak square
  Archive for Mathematical Logic 52 (2013), no.1-2, pp.29--45.
• (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.
• Partial square at omega_1 is implied by MM but not by PFA
  Fundamenta Mathematicae 215 (2011), pp.109--131.
• On standard model of Martin's Maximum
  RIMS Kokyuroku no.1754, pp.97-107, 2011.
• 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.
• Partial stationary reflection in P_{\omega_1} \omega_2
  RIMS Kokyuroku no.1595, pp.47-62, 2008.
• Semistationary and stationary reflection
  Journal of Symbolic Logic 73 (2008), no.1, pp.181-192.
• (with S. Fuchino, M. Karato and T. Usuba)
  \kappa^\kappa in light of Tukey ordering
  RIMS Kokyuroku no.1471, pp.19-34, 2006.
• Semiproper ideals
  Fundamenta Mathematicae 186 (2005), no.3, pp.251-267.
• Generalized Prikry forcing and iteration of generic ultrapowers
  Mathematical Logic Quarterly 51, no.5, pp.507-523, 2005.

Notes

• Martin's Maximum and stationary reflection at omega_3
• Semi-stationary reflection and weak square
• omega_1-stationary preserving poset of size omega_1 which is not semi-proper
• Pi^1_n+1-indescribability and simultaneous reflection of Pi^1_n-positive sets
• Note on least singular cardinal with cf( [lambda]^cf(lambda) , \subseteq ) > lambda^+
• TP and weak square
• Notes on skinny stationary subsets of P_\kappa \lambda
• Preservation of the failure of CG by finite support product of Cohen forcing
• Ideals over \omega_2 and combinatorical principles on \omega_1
• Weak diamond principle
• Completely bounding principle on P_\kappa \lambda
• Stationary reflection and 2^{\omega_1}
• Club guessing on P_\kappa \lambda

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