5 papers
Cardinal sequences and Cohen real extensions
István Juhász, Saharon Shelah, Lajos Soukup +1
We show that if we add any number of Cohen reals to the ground model then, in the generic extension, a locally compact scattered space has at most (2^{aleph_0})^V many levels of si…
Characterizing continuity by preserving compactness and connectedness
Janos Gerlits, Istvan Juhasz, Lajos Soukup +1
Let us call a function from a space into a space preserving if the image of every compact subspace of is compact in and the image of every connected subspace of…
A tall space with small bottom
Istvan Juhász, Saharon Shelah, Lajos Soukup +1
We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if kappa^{<kappa}…
On the weak Freese-Nation property of complete Boolean algebras
Sakaé Fuchino, Stefan Geschke, Saharon Shelah +1
The following results are proved: (a) In a model obtained by adding aleph_2 Cohen reals, there is always a c.c.c. complete Boolean algebra without the weak Freese-Nation property.…
Boolean algebras with prescribed topological densities
Lajos Soukup
We give a simplified proof of a theorem of M. Rabus and S. Shelah claiming that for each cardinal mu there is a c.c.c Boolean algebra with topological density mu.