arXiv subjects
Publications and source records attributed to Miroslav Zelen.
We introduce a family of forcing notions that are helpful in showing that certain graphs do not have countable colourings of (additive) Borel class alpha. We construct graphs that are ''weakly minimal'' for such colourings.
We study several natural classes of graphs on a zero-dimensional metrizable compact space having no continuous coloring. We compare these graphs with the quasi-order associated with injective continuous homomorphisms. We prove the existence of an antichain basis for these classes. We determine the size of such an antichain basis. We provide a concrete antichain basis when there is a countable one. We also provide some related quasi-orders and equivalence relations which are analytic complete as sets.