Frank Tall has worked in many areas of set-theoretic topology and set theory.

His current interests involve
a) applying forcing, large cardinals, selection principles, and topological games to classic problems concerning Lindelof
spaces,
b) applying models of form PFA(S)[S] to classic problems about paracompactness and metrizability in locally compact spaces, where a model is of form PFA(S)[S] if it is obtained by forcing with a coherent Souslin tree S over a model of
PFA restricted to those posets that preserve S. Such models are useful because in them hold many consequences of
PFA as well as some consequences of V = L.

Personal website


Recent and upcoming talks by Franklin Tall

Frank Tall: Completely Baire spaces, Menger spaces, projective sets, Hurewicz’ theorems, and an application to Model Theory

Place: Fields Institute (Room 210) Date: October 13, 2017 (13:30-15:00) Speaker: Frank Tall Title:Completely Baire spaces, Menger spaces, projective sets, Hurewicz’ theorems,  and an application to Model Theory Abstract: We prove the following are equiconsistent: (1) There is an inaccessible cardinal. continue reading…

Frontiers of Selection Principles, Warsaw, Aug 20 – Sep 1, 2017

The conference Frontiers of Selection Principles, celebrating the 60th birthday of Marion Scheepers will take place at the Dewajtis Campus, Bielanski forest, Warsaw, 20.8-1.9, 2017: 20.8-25.8 tutorial, 26.8 excursion, 27.8-1.9 conference. continue reading…

Franklin Tall: Arhangel’skii’s Lindelof points- $G_{\delta}$ problem

Place: Fields Institute (Room 210) Date: October 21st, 2016 (13:30-15:00) Speaker: Franklin Tall Title: Arhangel’skii’s Lindelof points- $G_{\delta}$ problem Abstract: My claim of a solution was premature. I will discuss the history of the problem, introduce n-dowments and the Mitchell collapse, and prove some results that could lead to a solution. continue reading…

Franklin Tall: Work in progress

Place: Fields Institute (Room 210) Date: September 23, 2016 (13:30-15:00) Speaker: Franklin Tall, University of Toronto Title: Work in progress Abstract: Depending on what I accomplish in the next week, I will either speak on the cardinality of regular Lindelof spaces with points $G_{\delta}$ or else on some connections among spaces satisfying the Baire Category Theorem, logics satisfying the Omitting Types Theorem, and non-meager P-filters. continue reading…

Franklin Tall: Non-metrizable descriptive set theory, generalized metric spaces, and selection principles

Place: Fields Institute (Room 210) Date: March 4th, 2016 (13:30-15:00) Speaker: Franklin Tall Title: Non-metrizable descriptive set theory, generalized metric spaces, and selection principles Abstract: This is a continuation of my most recent talk, but knowledge of that one is not required.  continue reading…

Franklin Tall: Definable Versions of Hurewicz’s Conjecture that Menger Spaces are Sigma-compact

Place: Fields Institute (Room 210) Date: January 29 , 2016 (13:30-15:00) Speaker: Franklin Tall Title: Definable Versions of Hurewicz’s Conjecture that Menger Spaces are Sigma-compact Abstract: Hurewicz’s conjecture that Menger spaces are sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for other definable subspaces of Polish spaces. continue reading…

Franklin Tall: PFA(S)[S] and countably compact spaces, continued

Place: Fields Institute (Room 210) Date: September 4th, 2015 (13:30-15:00) Speaker: Franklin Tall Title: PFA(S)[S] and countably compact spaces, continued Abstract: We continue with Alan Dow’s proof that PFA(S)[S] implies every first countable perfect pre-image of $\omega_1$ includes a copy of $\omega_1$. continue reading…

Franklin Tall: PFA(S)[S] and countably compact spaces

Place: Fields Institute (Room 210) Date: August 14th, 2015 (13:30-15:00) Speaker: Franklin Tall Title: PFA(S)[S] and countably compact spaces Abstract: We will continue with Dow’s proof and related material. continue reading…

Franklin Tall: PFA(S)[S] and countably compact spaces, II

Place: Fields Institute (Room 210) Date: July 31st, 2015 (13:30-15:00) Speaker: Franklin Tall Title: PFA(S)[S] and countably compact spaces, II Abstract: We give some more applications and then start going through the details of Alan’s proof.  continue reading…

Franklin Tall: PFA(S)[S] and copies of $\omega_1$

Place: Fields Institute (Room 210) Date: July 17th, 2015 (13:30-15:00) Speaker: Franklin Tall Title: PFA(S)[S] and copies of $\omega_1$ Abstract: Alan Dow proved PFA(S)[S] implies every first countable perfect preimage of $\omega_1$ includes a copy of $\omega_1$. continue reading…