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

A General Setting for the Pointwise Investigation of Determinacy

It is well-known that if we assume a large class of sets of reals to be determined then we may conclude that all sets in this class have certain regularity properties: we say that determinacy implies regularity properties classwise. In [Lö05] the pointwise relation between determinacy and certain regularity properties (namely the Marczewski-Burstin algebra of arboreal forcing notions and a corr...

On pointwise measurability of multifunctions

We present some results concerning pointwise measurability of multifunctions and some relationships with global measurability of multifunctions.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

1154 Jakob Kellner And

We present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. As an application, we introduce a new method to force (weak) measurability of all definable sets with respect to a certain (non-ccc) ideal.

Some Axioms of Weak Determinacy

We consider two-player games of perfect information of length some cardinal κ. It is well-known that for κ ≥ ω1 the full axiom of determinacy for these games fails, thus we investigate three weaker forms of it. We obtain the measurability of κ under DCκ-the axiom of dependent choices generalized to κ. We generalize the notions of perfect and meager sets and provide characterizations with some s...