ar X iv : m at h / 99 05 12 2 v 1 [ m at h . L O ] 1 9 M ay 1 99 9 THE CICHOŃ DIAGRAM

ar X iv : m at h / 99 05 11 4 v 1 [ m at h . L O ] 1 9 M ay 1 99 9 REMARKS ON THE INTERSECTION OF FILTERS

We will show that that the existence of an uncountable family of nonmeager filter whose intersection is meager is consistent with MA(Suslin).

ar X iv : m at h / 99 05 11 8 v 1 [ m at h . L O ] 1 9 M ay 1 99 9 REMARKS ON SETS RELATED TO TRIGONOMETRIC SERIES

We show that several classes of sets, like N 0-sets, Arbault sets, N-sets and pseudo-Dirichlet sets are closed under adding sets of small size.

ar X iv : m at h / 99 05 12 0 v 1 [ m at h . L O ] 1 9 M ay 1 99 9 BOREL IMAGES OF SETS OF REALS

The main goal of this paper is to generalize several results concerning cardinal invariants to the statements about the associated families of sets. We also discuss the relationship between the additive properties of sets and their Borel images. Finally, we present estimates for the size of the smallest set which is not strongly meager.

ar X iv : m at h / 99 05 00 1 v 1 [ m at h . A G ] 1 M ay 1 99 9 Tacnodes and cusps

ar X iv : h ep - p h / 99 05 24 9 v 2 1 2 M ay 1 99 9 BI - TP 99 / 12 Two - loop self - energy master integrals on shell

Analytic results for the complete set of two-loop self-energy master integrals on shell with one mass are calculated.