9 citations · 44 across the 28 of their papers we have counts for
6 papers · 1 filter
Definable versions of Menger's conjecture
Franklin D. Tall
Menger's conjecture that Menger spaces are /sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for more complex definable subspaces of Polis…
Hereditarily normal manifolds of dimension > 1 may all be metrizable
Alan Dow, Franklin D. Tall
P.J. Nyikos has asked whether it is consistent that every hereditarily normal manifold of dimension > 1 is metrizable, and proved it is if one assumes the consistency of a supercom…
On the definability of Menger spaces which are not /sigma-compact
Franklin D. Tall, Secil Tokgoz
Hurewicz proved completely metrizable Menger spaces are /sigma-compact. We extend this to Cech-complete Menger spaces and consistently to projective Menger metrizable spaces. On th…
PFA(S)[S] for the masses
Franklin D. Tall
We present S. Todorcevic's method of forcing with a coherent Souslin tree over restricted iteration axioms as a black box usable by those who wish to avoid its complexities but sti…
PFA(S)[S] and countably compact spaces
Alan Dow, Franklin D. Tall
We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S)[S]. We also show the consistency without large cardinals of "every locally compact,…
Normality versus paracompactness in locally compact spaces
Alan Dow, Franklin D. Tall
This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing…