We define the property of Π2-compactness of a statement φ of set theory, meaning roughly that the hard core of the impact of φ on combinatorics of א1 can be isolated in a canonical model for the statement φ. We show that the following statements are Π2compact: “dominating number= א1,” “cofinality of the meager ideal= א1”, “cofinality of the null ideal= א1”,“bounding number= א1”, existence of va...

We define the property of Π2-compactness of a statement φ of set theory, meaning roughly that the hard core of the impact of φ on combinatorics of א1 can be isolated in a canonical model for the statement φ. We show that the following statements are Π2compact: “dominating number= א1,” “cofinality of the meager ideal= א1”, “cofinality of the null ideal= א1”,“bounding number= א1”, existence of va...

We present ROSAT HRI observations of six quasars with redshifts >∼3.4: PKS 0335-122, S4 0620+389, B1422+231, PKS 2215+02, Q 2239-386 and PC 2331+0216. We include the observation of the radio-quiet quasar BG 57 9, whose redshift has recently been revised to z = 0.965. S4 0620+389, B1422+231, PKS 2215+02 and BG 57 9 are detected in the ROSAT energy band (0.1-2.4 keV). 2σ upper limits are given fo...

The linear quadratic optimal regulator problem on a wave equation in a bounded subset of R for n = 2; 3 with boundary damping and pointwise control input is formulated as a linear quadratic control problem with unbounded input/output operators using a variational approach. A dual control system is de ned which allows us to investigate the regularity of the solution of the generalized wave equat...