Dilip Raghavan

Office location: S17-07-15

Mailing Address:
Department of Mathematics
10 Lower Kent Ridge Road
Singapore 119076

Email Addresses:


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Research interests

Mathematical Logic, Set Theory, Infinitary Ramsey Theory, and General Topology.

Curriculum Vitae

Papers

  1. (with K. Kunen) Gregory Trees, the Continuum, and Martin's Axiom, J. Symbolic Logic, vol. 74 (2009), no. 2, 712--720.
  2. Maximal almost disjoint families of functions, Fund. Math., vol. 204 (2009), no. 3, 241--282.
  3. There is a Van Douwen mad family, Trans. Amer. Math. Soc., vol. 362 (2010), no. 11, 5879--5891.
  4. Almost disjoint families and diagonalizations of length continuum, Bull. Symbolic Logic, vol. 16 (2010), no. 2, 240--260.
  5. A model with no strongly separable almost disjoint families, Israel J. Math., vol. 189 (2012), no. 1, 39--53.
  6. (with J. Steprāns) On weakly tight families, Canad. J. Math., vol. 64 (2012), no. 6, 1378--1394.
  7. (with S. Todorcevic) Cofinal types of ultrafilters, Ann. Pure Appl. Logic, vol. 163 (2012), no. 3, 185--199.
  8. (with S. Shelah) Comparing the closed almost disjointness and dominating numbers, Fund. Math., vol. 217 (2012), no. 1, 73--81.
  9. P-ideal dichotomy and weak squares, J. Symbolic Logic, vol. 78 (2013), no. 1, 157--167.
  10. (with T. Yorioka) Suslin lattices, Order, vol. 31 (2014), no. 1, 55--79.
  11. (with H. Mildenberger and J. Steprāns) Splitting families and complete separability, Canad. Math. Bull., vol. 57 (2014), no. 1, 119--124.
  12. (with J. Brendle) Bounding, splitting, and almost disjointness, Ann. Pure Appl. Logic, vol. 165 (2014), no. 2, 631--651.
  13. (with S. Todorcevic) Combinatorial dichotomies and cardinal invariants, Math. Res. Lett., vol. 21 (2014), no. 2, 379--401.
  14. (with A. Blass and N. Dobrinen) The next best thing to a P-point, J. Symbolic Logic, vol. 80 (2015), no. 3, 866--900.
  15. (with S. Shelah) On embedding certain partial orders into the P-points under RK and Tukey reducibility, Trans. Amer. Math. Soc., vol. 369 (2017), no. 6, 4433--4455.
  16. (with S. Shelah) Two inequalities between cardinal invariants, Fund. Math., vol. 237 (2017), no. 2, 187--200.
  17. (with P. B. Larson) Real games and strategically selective coideals, in Sets and computations, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., vol. 33 (2017), pp. 45--54.
  18. (with R. Hölzl, F. Stephan, and J. Zhang) Weakly represented families in reverse mathematics, in Computability and complexity, Lecture Notes in Comput. Sci., vol. 10010 (2017), Springer, Cham., pp. 160--187.
  19. (with S. Todorcevic) Suslin trees, the bounding number, and partition relations, Israel J. Math., vol. 225 (2018), no. 2, 771--796.
  20. (with B. Kuzeljevic) A long chain of P-points, J. Math. Log., vol. 18 (2018), no. 1, 1850004, 38 pp.
  21. (with S. Shelah) Two results on cardinal invariants at uncountable cardinals, in Proceedings of the 14th and 15th Asian Logic Conferences (Edited by: B. Kim, J. Brendle, G. Lee, F. Liu, R. Ramanujam, S. M. Srivastava, A. Tsuboi, and L. Yu), World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2019), pp. 129--138.
  22. (with J. L. Verner) Chains of P-points, Canad. Math. Bull., vol. 62 (2019), no. 4, 856--868.
  23. (with S. Shelah) A small ultrafilter number at smaller cardinals, Arch. Math. Logic, vol. 59 (2020), no. 3--4, 325--334.
  24. The density zero ideal and the splitting number, Ann. Pure Appl. Logic, vol. 171 (2020), no. 7, 102807, 15pp.
  25. (with K. Higuchi, S. Lempp, and F. Stephan) On the order dimension of locally countable partial orderings, Proc. Amer. Math. Soc., vol. 148 (2020), no. 7, 2823--2833.
  26. (with S. Todorcevic) Proof of a conjecture of Galvin, Forum of Mathematics, Pi, vol. 8 (2020), E15, 1--23.
  27. (with A. Kumar) Separating families and order dimension of Turing degrees, Ann. Pure Appl. Logic (special issue marking the 50th Anniversary of the Toronto Set Theory Seminar), vol. 172 (2021), no. 5, 102911, 20 pp.
  28. (with R. Johnston) Complexity of index sets of descriptive set-theoretic notions, J. Symbolic Logic, vol. 87 (2022), no. 3, 894--911.
  29. (with S. Todorcevic) A combinatorial property of rho-functions, Acta Math. Hungar., vol. 167 (2022), no. 1, 355--363.
  30. (with J. Steprāns) The almost disjointness invariant for products of ideals, Topology Appl., vol. 323 (2023), 108295, 8 pp.
  31. (with A. Kumar) Supersaturated ideals, Topology Appl., vol. 323 (2023), 108289, 12 pp.
  32. (with S. Todorcevic) Galvin’s problem in higher dimensions, Proc. Amer. Math. Soc., vol. 151 (2023), no. 7, 3103--3110.
  33. (with B. Kuzeljevic and J. L. Verner) Lower bounds of sets of P-points, Notre Dame J. Form. Log., vol. 64 (2023), no. 3, 317--327.
  34. (with J. Brendle, O. Guzmán, and M. Hrušák) Combinatorial properties of MAD families, submitted.
  35. (with J. Steprāns) Stable ordered-union versus selective ultrafilters, submitted.
  36. (with B. Kuzeljevic) Order structure of P-point ultrafilters and their relatives, submitted.
  37. (with J. Steprāns) Nowhere dense ultrafilters and some weak forms of selectivity, submitted.
  38. (with M. Xiao) Borel order dimension, submitted.
  39. (with P. B. Larson) A combinatorial property of ultrafilters in L(R)[U], in preparation.
  40. (with S. Shelah) On the reaping number at the first Mahlo cardinal, in preparation.
  41. (with S. Shelah) Boolean ultrapowers and iterated forcing, in preparation.

Upcoming and Recent Talks

Teaching

Fall 2024