A hodgepodge of sets of reals

Abstract

We prove a variety of results concerning singular sets of reals. Our results concern: Kysiak and Laver-null sets, Kocinac and gamma-k-sets, Fleissner and square Q-sets, Alikhani-Koopaei and minimal Q-like-sets, Rubin and sigma-sets, and Zapletal and the Souslin number. In particular we show that sigma-sets are Laver-null, the union of gamma-k-sets need not be gamma-k, the existence of Q-set implies an omega1-universal G_delta, minimal Q-like sets which are not Q-sets exist, thin sets need not exist, and sn* is bounded by the cardinality of the smallest nonmeager set.