arXiv subjects

Bohuslav Balcar

Publications and source records attributed to Bohuslav Balcar.

3 recordsLinked to original sources

arXiv2013

Base Tree Property

Building on previous work of [BPS] we investigate $σ$-closed partial orders of size continuum. We provide both an internal and external characterization of such partial orders by showing that (1) every $σ$-closed partial order of size continuum has a base tree and that (2) $σ$-closed forcing notions of density $\mathfrak c$ correspond exactly to regular suborders of the collapsing algebra $Coll(ω_1, 2^ω)$. We further study some naturally ocurring examples of such partial orders.

math.LO↗

arXiv1996

The sequential topology on complete Boolean algebras

We investigate the sequential topology $τ_s$ on a complete Boolean algebra $B$ determined by algebraically convergent sequences in $B$. We show the role of weak distributivity of $B$ in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for $B$ to carry a strictly positive Maharam submeasure is that $B$ is ccc and that the space $(B,τ_s)$ is Hausdorff. We also characterize sequential cardinals.

math.LO↗

arXiv1995

Semi-Cohen Boolean algebras

We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A >>Cohen algebra<< is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semi-Cohen algebras, pseudo-Cohen algebras and potentially Cohen algebras. These classes of Boolean algebras are closed under completion.

math.LO↗