Dan Hathaway

A simple C*-algebra with finite nuclear dimension which is not Z-stable

We construct a simple C*-algebra with nuclear dimension zero that is not isomorphic to its tensor product with the Jiang-Su algebra Z, and a hyperfinite II_1 factor not isomorphic to its tensor product with the separable hyperfinite II_1 factor R. The proofs use a weakening of the Continuum Hypothesis.

Disjoint Borel functions

For each

WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY

a \in \mathbb{R}

Combinatorics of reductions between equivalence relations

, we define a Borel function

THE HALPERN–LÄUCHLI THEOREM AT A MEASURABLE CARDINAL

f_a : \mathbb{R} \to \mathbb{R}

A Lower Bound for Generalized Dominating Numbers

which encodes

Sacks Forcing and the Shrink Wrapping Property

a

Generic Coding with Help and Amalgamation Failure

in a certain sense. We show that for each Borel

Ramsey theory on generalized Baire space

g : \mathbb{R} \to \mathbb{R}

Forcing and the Halpern-L\"auchli Theorem

,