The Pointwise View of Determinacy: Arboreal Forcings, Measurability and Weak Measurability
Benedikt Löwe

Abstract:
We prove that for all standard arboreal forcing notions P there is a
counterexample for the implication "If A is determined, then A is
P-measurable". Moreover, we investigate for which forcing notions this
is extendible to "weakly P-measurable".

Keywords: Trees, Games, Determinacy, Forcing