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

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…

Frank Tall: PFA(S)[S] III

Place: Fields Institute (Room 210) Date: July 3rd (13:30- 15:00) Speaker: Franklin Tall Title: PFA(S)[S] III Abstract: I will use the machinery developed last time plus a little topology to finish the proof. continue reading…

Franklin Tall: PFA(S)[S] II

Place: Fields Institute (Room 210) Date:  26-June-2015 (13:30-14:45) Speaker: Franklin Tall Title: PFA(S)[S] II Abstract: This is a continuation of last week’s lecture. Last week’s lecture was largely motivation; this lecture will be mainly technical, developing the method. continue reading…