Solovay's inaccessible over a weak set theory without choice

We study the consistency strength of Lebesgue measurability for $\Sigma^1_3$ sets over a weak set theory in a completely choiceless context. We establish a result analogous to the Solovay-Shelah theorem

Martin's maximum and the non-stationary ideal

We analyze the non-stationary ideal and the club filter at aleph_1 under MM

Updated Limits on TeV-Scale Gravity from Absence of Neutrino Cosmic Ray Showers Mediated by Black Holes

We revise existing limits on the D-dimensional Planck scale M_D from the nonobservation of microscopic black holes produced by high energy cosmic neutrinos in scenarios with D=4+n large extra dimensions. Previous studies have neglected the energy radiated in gravitational waves by the multipole moments of the incoming shock waves. We include the effects of energy loss, as well as form factors for black hole production and recent null results from cosmic ray detectors. For n>4, we obtain M_D > 1.0 - 1.4 TeV. These bounds are among the most stringent and conservative to date.Comment: 11 pages, 4 figure