17 citations · 39 across the 7 of their papers we have counts for
12 papers · 1 filter
Condensed Whitehead Problem
Spencer Unger, Jerry Wei
The Whitehead problem, which asks whether every abelian group satisfying is free, is independent of ZFC. However, this problem has an analogu…
Circle Squaring
Spencer Unger, Narmada Varadarajan, Felix Weilacher
We show that a circle and square of the same area in are equidecomposable by translations using pieces. That is, pieces which are simultaneously …
Oscillating subalgebras of the atomless countable Boolean algebra
Dana Bartošová, David Chodounský, Barbara Csima +6
We show that the big Ramsey degree of the Boolean algebra with 3 atoms within the countable atomless Boolean algebra is infinite.
Stationary Reflection and the failure of SCH
Omer Ben-Neria, Yair Hayut, Spencer Unger
In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal such that the singular cardinal hypothesis fails at and eve…
Measurable realizations of abstract systems of congruences
Clinton T. Conley, Andrew S. Marks, Spencer T. Unger
An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congrue…
Stationary Reflection
Yair Hayut, Spencer Unger
We improve the upper bound for the consistency strength of stationary reflection at successors of singular cardinals.
Successive failures of approachability
Spencer Unger
Motivated by showing that in ZFC we cannot construct a special Aronszajn tree on some cardinal greater than , we produce a model in which the approachability property fai…
Borel Circle Squaring
Andrew S. Marks, Spencer T. Unger
We give a completely constructive solution to Tarski's circle squaring problem. More generally, we prove a Borel version of an equidecomposition theorem due to Laczkovich. If $k \g…
Diagonal supercompact Radin forcing
Omer Ben-Neria, Chris Lambie-Hanson, Spencer Unger
Motivated by the goal of constructing a model in which there are no -Aronszajn trees for any regular , we produce a model with many singular cardinals where both the…
The strong tree property and weak square
Yair Hayut, Spencer Unger
We show that it is consistent, relative to many supercompact cardinals, that the super tree property holds at for all but there are weak square and a…
Large Cardinal Axioms from Tameness in AECs
Will Boney, Spencer Unger
We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions.
Baire measurable paradoxical decompositions via matchings
Andrew Marks, Spencer Unger
We show that every locally finite bipartite Borel graph satisfying a strengthening of Hall's condition has a Borel perfect matching on some comeager invariant Borel set. We apply t…