The ultrafilter number for singular cardinals

We prove the consistency of a singular cardinal $\lambda$ with small value of the ultrafilter number $u_\lambda$, and arbitrarily large value of $2^\lambda$.Comment: 8 page

The character of topological groups, via bounded systems, Pontryagin--van Kampen duality and pcf theory

The Birkhoff--Kakutani Theorem asserts that a topological group is metrizable if and only if it has countable character. We develop and apply tools for the estimation of the character for a wide class of nonmetrizable topological groups. We consider abelian groups whose topology is determined by a countable cofinal family of compact sets. These are the closed subgroups of Pontryagin--van Kampen duals of \emph{metrizable} abelian groups, or equivalently, complete abelian groups whose dual is metrizable. By investigating these connections, we show that also in these cases, the character can be estimated, and that it is determined by the weights of the \emph{compact} subsets of the group, or of quotients of the group by compact subgroups. It follows, for example, that the density and the local density of an abelian metrizable group determine the character of its dual group. Our main result applies to the more general case of closed subgroups of Pontryagin--van Kampen duals of abelian \v{C}ech-complete groups. In the special case of free abelian topological groups, our results extend a number of results of Nickolas and Tkachenko, which were proved using combinatorial methods. In order to obtain concrete estimations, we establish a natural bridge between the studied concepts and pcf theory, that allows the direct application of several major results from that theory. We include an introduction to these results and their use.Comment: Minor corrections. Final version before journal editin

Indestructibility of Vopenka's Principle

We show that Vopenka's Principle and Vopenka cardinals are indestructible under reverse Easton forcing iterations of increasingly directed-closed partial orders, without the need for any preparatory forcing. As a consequence, we are able to prove the relative consistency of these large cardinal axioms with a variety of statements known to be independent of ZFC, such as the generalised continuum hypothesis, the existence of a definable well-order of the universe, and the existence of morasses at many cardinals.Comment: 15 pages, submitted to Israel Journal of Mathematic

Centrally Administered Pertussis Toxin Inhibits Microglia Migration to the Spinal Cord and Prevents Dissemination of Disease in an EAE Mouse Model

Background: Experimental autoimmune encephalomyelitis (EAE) models are important vehicles for studying the effect of infectious elements such as Pertussis toxin (PTx) on disease processes related to acute demyelinating encephalomyelitis (ADEM) or multiple sclerosis (MS). PTx has pleotropic effects on the immune system. This study was designed to investigate the effects of PTx administered intracerebroventricularly (icv) in preventing downstream immune cell infiltration and demyelination of the spinal cord. Methods and Findings: EAE was induced in C57BL/6 mice with MOG35–55. PTx icv at seven days post MOG immunization resulted in mitigation of clinical motor symptoms, minimal T cell infiltration, and the marked absence of axonal loss and demyelination of the spinal cord. Integrity of the blood brain barrier was compromised in the brain whereas spinal cord BBB integrity remained intact. PTx icv markedly increased microglia numbers in the brain preventing their migration to the spinal cord. An in vitro transwell study demonstrated that PTx inhibited migration of microglia. Conclusion: Centrally administered PTx abrogated migration of microglia in EAE mice, limiting the inflammatory cytokine milieu to the brain and prevented dissemination of demyelination. The effects of PTx icv warrants further investigation and provides an attractive template for further study regarding the pleotropic effects of infectious elements such as PTx in th