Department of Mathematics
University of Toronto

Franklin D. Tall

Ph.D. 1969 (Wisconsin)

Department of Mathematics
University of Toronto
Toronto, ON M5S 3G3
Tel: (416) 978-3953 or (905) 828-3812
Fax: (416) 978-4107 or (905) 569-4730


Frank Tall specializes in set theory and set-theoretic topology, fields in which he has authored around 90 papers. Of his 12 Ph.D. students, 9 are on university faculties: Indianapolis, Toronto, York (3), McMaster, P.E.I., São Paulo (2). His postdocs are at universities such as Winnipeg, Toronto, Trent, Haifa, Ohio, Calgary, and McMaster.

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, is trained in hypnotherapy, a Reiki Master and has published in Nursing Science.


  1. F.D. Tall, Productively Lindelof spaces may all be D Canad. Math. Bull. to appear.
  2. F.D. Tall, Some set-theoretic problems concerning Lindelof spaces Questions and Answers in General Topology to appear.
  3. F.D. Tall, PFA(S)[S]: more mutually consistent topological consequences of PFA and V = L Canad. J. Math. to appear.
  4. P. Larson and F.D. Tall, On the hereditary paracompactness of locally compact, hereditarily normal spaces Canad. Math. Bull. to appear.
  5. F.D. Tall, PFA(S)[S] and locally compact normal spaces Top. Appl. to appear.
  6. P. Burton and F.D. Tall, Productive Lindelofness and a class of spaces considered by Z. Frolik Top. Appl. to appear.
  7. F.D. Tall, A Useful Model (notes).
  8. F.D. Tall, A Useful Model (slides).

Some recent publications include:

  1. L.F. Aurichi and F.D. Tall, Lindelof spaces which are indestructible, productive or D Top. Appl. 159 (2012) 331–340.
  2. F.D. Tall, PFA(S)[S] and the Arhangel'skii-Tall problem Top. Proc. 40 (2012) 99-108.
  3. F.D. Tall and B. Tsaban, On productively Lindelof spaces, Top. Appl. 158 (2011) 1239–1248.
  4. 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.
  5. F.D. Tall, Lindelof spaces which are Menger, Hurewicz, Alster, productive or D Top. Appl. 158 (2011) 2556-2563.
  6. 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
  7. P. Larson and F.D. Tall, Locally compact perfectly normal spaces may all be paracompact Fund. Math. 210 (2010) 285-300
  8. M. Scheepers and F.D. Tall, Lindelof indestructibility, topological games and selection principles Fund. Math. 210 (2010) 1-46
  9. F.D. Tall, On a core concept of Arhangel'skii Top. Appl. 157 (2010) 1541-1547
  10. L.-X. Peng and F.D. Tall, A note on linearly Lindelof spaces and dual properties Top. Proc. 32 (2008) 227-237
  11. 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
  12. F.D. Tall, Compact Spaces, Elementary Submodels, and the Countable Chain Condition, II, Top. Appl., 153 (2004) 273-278.
  13. F.D. Tall, Problems arising from Balogh's "Locally nice spaces under Martin's axiom", Top. Appl., 5 (2005) 215-225.
  14. 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.
  15. F.D. Tall, Reflections on dyadic compacta, Top. Appl., 137 (2004) 251-258.
  16. 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.
  17. 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.
  18. L.R. Junqueira and F.D. Tall, More reflections on compactness, Fund. Math., 176 (2003) 127-141.
  19. F.D. Tall, An irrational problem, Fund. Math., 175 (2002) 259-269.
  20. P. Koszmider and F.D. Tall, A Lindelof space with no Lindelof subspace of size w1 , Proc. Amer. Math. Soc., 130 (2002) 2777-2787.
  21. J.E. Baumgartner and F.D. Tall, Reflecting Lindelofness, Top. Appl., 12 (2002) 35-49.
  22. 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.
  23. F.D. Tall, If it looks and smells like the reals, Fund. Math. 163 (2000) 1-11. (Available from Topology Atlas.)
  24. 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 2011

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