The Axiom of Determinacy holds in the inner model L(R) assuming Martin’s Maximum for partial orderings of size c.

The developments of set theory in 1960’s led to an era of independence in which many of the central questions were shown to be unresolvable on the basis of the standard system of mathematics, ZFC. This is true of statements from areas as diverse as analysis (“Are all projective sets Lebesgue measurable?”), cardinal arithmetic (“Does Cantor’s Continuum Hypothesis hold?”), combinatorics (“Does Su...

A singularity is described that creates a forward time loss of determinacy in two-timescale system, the limit where timescale separation large. We describe how situation can arise dynamical system two fast variables and three slow or parameters, with weakly coupling between variables. wide set initial conditions enters [Formula: see text]-neighborhood singularity, explodes back out it to fill l...