Department of Mathematics
University of Toronto

Franklin D. Tall

Professor Emeritus
Ph.D. 1969 University of Wisconsin (Madison)

Department of Mathematics
University of Toronto
Toronto, ON M5S 2E4
Tel: (416) 978-3323
Fax: (416) 978-4107


Frank Tall specializes in set theory and set-theoretic topology, fields in which he has authored around 100 papers. Lately, he and his students have been working on applications of topology to model theory. Of his 14 Ph.D. students, 9 are on university faculties: Indianapolis, Toronto, York (3), McMaster, P.E.I., São Paulo, Victoria. His postdocs are at universities such as Winnipeg, São Paulo, Monterey (Mexico), Trent, Waterloo, Calgary, and North Carolina (Charlotte).

In addition to mathematics, he is interested in the psychology of teaching and learning, and complementary medicine. He is a certified Master Practitioner of Neurolinguistic Programming, a Reiki Master, is trained in hypnotherapy and has published in Nursing Science. He is currently researching the effects of light-and-sound stimulation on mental state.


  1. F.D. Tall and J. Zhang, The second order version of Morley's theorem on the number of countable models does not require large cardinals, Arch. Math. Logic, to appear.
  2. C. Hamel and F.D. Tall, On the undefinability of pathological Banach spaces, submitted.
  3. I. Ongay-Valverde and F.D. Tall, A new topological generalization of descriptive set theory.

Some recent publications include:

  1. C.J. Eagle, C. Hamel, S. Müller, F.D. Tall, An undecidable extension of Morley's theorem on the number of countable models Ann. Pure Appl. Logic 174:9 (2023), Paper No. 103317.
  2. F.D. Tall, Countable tightness and the Grothendieck property in Cp-theory Top. Appl. 323 (2023), Paper No. 108299.
  3. C. Hamel and F.D. Tall, Cp-theory for model theorists. In Beyond First Order Model Theory, v. II, ed. J. Iovino, CRC Press, Boca Raton (2023), 177-214.
  4. C. Hamel, C.J. Eagle, and F.D. Tall, Two applications of topology to model theory Ann. Pure Appl. Logic 172:5 (2021), Paper No. 102907.
  5. F. D. Tall, S. Todorcevic, and S. Tokgöz, The strength of Menger's conjecture Top. Appl. 301 (2021), Paper No. 107536.
  6. F.D. Tall, Co-analytic spaces, K-analytic spaces, and definable versions of Menger's conjecture Top. Appl. 283 (2020), Paper No. 107345.
  7. C. Hamel and F.D. Tall, Model theory for Cp-theorists Top. Appl. (2020),
  8. A. Dow and F.D. Tall, Hereditarily normal manifolds of dimension greater than one may all be metrizable Trans. Amer. Math. Soc. 372 (2019) 6805-6851.
  9. F.D. Tall and L. Zdomskyy, Completely Baire spaces, Menger spaces, and projective sets Top. Appl. 258 (2019) 26-31.
  10. A. Dow and F.D. Tall, Normality versus paracompactness in locally compact spaces, Canad. J. Math. 70 (2018) 74-96.
  11. F.D. Tall, PFA(S)[S] for the masses, Top. Appl. 232 (2017) 13-21.
  12. A. Dow and F.D. Tall, PFA(S)[S] and countably compact spaces, Top. Appl. 210 (2017) 393-416.
  13. F.D. Tall and S. Tokgöz, On the definability of Menger spaces which are not σ-compact, Top. Appl. 220 (2017) 111-117.
  14. F.D. Tall, Some observations on the Baireness of Ck(X) for a locally compact space X, Top. Appl. 213 (2016) 212-219.
  15. A.J. Fischer, F.D. Tall, and S. Todorcevic, Forcing with a coherent Souslin tree and locally countable subspaces of countably tight compact spaces, Top. Appl. 195 (2015) 284-296.
  16. F.D. Tall and T. Usuba, Lindelöf spaces with small pseudocharacter and an analogy of Borel's conjecture for subsets of [0,1]1 Houston J. Math. 40 (2014) 1299-1309.
  17. P. Larson and F.D. Tall, On the hereditary paracompactness of locally compact, hereditarily normal spaces Canad. Math. Bull. 57 (2014) 579-584.
  18. F.D. Tall, PFA(S)[S] and locally compact normal spaces Top. Appl. 162 (2014) 100-115.
  19. H. Duanmu, F.D. Tall, and L. Zdomskyy, Productively Lindelöf and indestructibly Lindelöf spaces, Top. Appl. 165 (2013) 2443-2453.
  20. R.R. Dias and F.D. Tall, Indestructibility of compact spaces, Top. Appl. 160 (2013) 2411-2426.
  21. F.D. Tall, PFA(S)[S]: more mutually consistent topological consequences of PFA and V = L Canad. J. Math. 64 (2012) 1182-1200.
  22. P. Burton and F.D. Tall, Productive Lindelöfness and a class of spaces considered by Z. Frolík Top. Appl. 159 (2012) 3097-3102.
  23. F.D. Tall, Some set-theoretic problems concerning Lindelöf spaces Questions and Answers in Gen. Top. 29 (2011) 91-103.
  24. L.F. Aurichi and F.D. Tall, Lindelof spaces which are indestructible, productive or D Top. Appl. 159 (2012) 331-340.
  25. F.D. Tall, PFA(S)[S] and the Arhangel'skii-Tall problem Top. Proc. 40 (2012) 99-108.
  26. F.D. Tall and B. Tsaban, On productively Lindelof spaces, Top. Appl. 158 (2011) 1239-1248.
  27. O.T. Alas, L.F. Aurichi, L.R. Junqueira, and F.D. Tall, Non-productively Lindelof spaces and small cardinals Houston J. Math. 37 (2011) 1373-1381.
  28. F.D. Tall, Lindelof spaces which are Menger, Hurewicz, Alster, productive or D Top. Appl. 158 (2011) 2556-2563.
  29. F.D. Tall, Some problems and techniques in set-theoretic topology In Set Theory and its Applications Contemp. Math., ed. L. Babinkostova, A. Caicedo, S. Geschke, M. Scheepers. (2011) 183-209
  30. P. Larson and F.D. Tall, Locally compact perfectly normal spaces may all be paracompact Fund. Math. 210 (2010) 285-300
  31. M. Scheepers and F.D. Tall, Lindelof indestructibility, topological games and selection principles Fund. Math. 210 (2010) 1-46
  32. F.D. Tall, On a core concept of Arhangel'skii Top. Appl. 157 (2010) 1541-1547
  33. L.-X. Peng and F.D. Tall, A note on linearly Lindelof spaces and dual properties Top. Proc. 32 (2008) 227-237
  34. L.R. Junqueira, P. Larson, and F.D. Tall, Compact Spaces, elementary submodels, and the countable chain condition Ann. Pure and Applied Logic,144 (2006) 107-116
  35. F.D. Tall, Compact Spaces, Elementary Submodels, and the Countable Chain Condition, II, Top. Appl., 153 (2004) 273-278.
  36. F.D. Tall, Problems arising from Balogh's "Locally nice spaces under Martin's axiom", Top. Appl., 5 (2005) 215-225.
  37. Y.Q. Qiao and F.D. Tall, Perfectly normal non-Archimedean non-metrizable spaces are generalized Souslin lines, Proc. Amer. Math. Soc., 131 (2003) 3929-3936.
  38. F.D. Tall, Reflections on dyadic compacta, Top. Appl., 137 (2004) 251-258.
  39. F.D. Tall, Consistency results in topology, II: Forcing and large cardinals, (invited paper), 423-427 in The Encyclopedia of General Topology, Elsevier, New York, 2003.
  40. K.P. Hart and F.D. Tall, Consistency results in topology, I: Quotable principles, 419-422 in The Encyclopedia of General Topology, Elsevier, New York, 2003.
  41. L.R. Junqueira and F.D. Tall, More reflections on compactness, Fund. Math., 176 (2003) 127-141.
  42. F.D. Tall, An irrational problem, Fund. Math., 175 (2002) 259-269.
  43. P. Koszmider and F.D. Tall, A Lindelof space with no Lindelof subspace of size w1 , Proc. Amer. Math. Soc., 130 (2002) 2777-2787.
  44. J.E. Baumgartner and F.D. Tall, Reflecting Lindelofness, Top. Appl., 12 (2002) 35-49.
  45. R.G.A. Prado and F.D. Tall, Characterizing w1 and the long line by their topological elementary reflections, Israel J. Math., 127 (2002) 81-94.
  46. F.D. Tall, If it looks and smells like the reals, Fund. Math. 163 (2000) 1-11. (Available from Topology Atlas.)
  47. K. Kunen and F.D. Tall, The real line in elementary submodels of set theory, J. Symb. Logic 65 (2000) 683-691. (Available from Topology Atlas.)
(Papers are linked to .pdf files.)

Last Updated: March 2024

Math Home