SAKAI, Hiroshi

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Title
Professor
Field
Mathematical Logic, Set Theory
Research interests
Large Cardina Axioms, Forcing Axioms and their consequences in infinite combinatorics and cardinal arithmetic
Current research

The standard axiom system ZFC of set theory is a comprehensive axiom system in which almost all standard mathematics can be formalized. But it is known that many mathematical propositions on infinity, such as the Continuum Hypothesis, are not decidable in ZFC. I am investigating what can be proved in various expansions of ZFC. Especially, I am interested in expansions of ZFC by Large Cardinal Axioms, Forcing Axioms and Reflection Principles.
Selected publications
  1. S. Fuchino, A.O.M. Rodorigues and H. Sakai, Strong downward Lowenheim-Skolem therorems for stationary logics, II. Archive for Mathematical Logic 60 (2021), no.3-4, 495-523.
  2. S. Fuchino, A.O.M. Rodorigues and H. Sakai, Strong downward Lowenheim-Skolem therorems for stationary logics, I. Archive for Mathematical Logic 60 (2021), no.1-2, 17-47.
  3. H. Sakai, On Katetov and Katetov-Blass orders on analytic P-ideals and Borel ideals. Archive for Mathematical Logic 57 (2018), no.3-4, 317-327.
  4. J. Bagaria, M. Magidor and H. Sakai, Reflection and indescribability in the constructible universe. Israel Journal of Mathematics 208 (2015), 1-11.
  5. H. Sakai, Simple proofs of SCH from reflection principles without using better scales. Archive for Mathematical Logic 54 (2015), no.5, 639-647.
  6. H. Sakai and B. Velickovic, Stationary reflection principles and two cardinal tree properties. Journal of the Institute of Mathematics of Jussieu 14 (2015), no.1, 69-85.
  7. H. Sakai, Chang's conjecture and weak square. Archive for Mathematical Logic 52 (2013), no.1-2, 29-45.
  8. H. Sakai, Semistationary and stationary reflection. Journal of Symbolic Logic 73 (2008), no.1, 181-192.
  9. H. Sakai, Semiproper ideals. Fundamenta Mathematicae 186 (2005), no.3, pp.251-267.

Memberships, activities and

Awards

The Mathematical Society of Japan

Association for Symbolic Logic

Editor of The Journal of Symbolic Logic (2020-)

Councilor of The Mathematical Society of Japan (2022-2024)