A topology generated by eventually different functions
We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree -base for with no branches yet of height . We establish that this is also possible for using a natural modification of Mathias forcing.
We construct a universal planar completely regular continuum. This gives a positive answer to a problem posed by J. Krasinkiewicz (1986).
Let be a -semigroup with unbounded generator . We prove that has generically a very irregular behaviour for as .