Jakob Kellner

Decisive creatures and large continuum

† Abstract. Forf,g ∈ u u letc ∀ f,g be the minimal number of uniformg-splitting trees (or: Slaloms) to cover the uniformf-splitting tree, i.e., for every branchiof thef-tree, one of theg-trees containsi. c ∃ f,g is the dual notion: For every branchi, one of theg-trees guessesi(m) infinitely often. It is consistent thatc ∃ fǫ,gǫ =c ∀ fǫ,gǫ =κǫ for ℵ1 manypairwise different cardinalsκǫ and suitable pairs (fǫ,gǫ). For the proof we use creatures with sufficient bigness and halving. We show that the lim-inf creature forcing satisfies fusion and pure decision. We introduce decisiveness and use it to construct a variant of the countable support iteration of such forcings, which still satisfies fusion and pure decision.

Creature forcing and large continuum: the joy of halving

For

Borel conjecture and dual Borel conjecture

{f,g\in\omega^\omega}

Pitowsky’s Kolmogorovian Models and Super-determinism

let

Compact Cardinals and eight Values in Cichoń's Diagram.

{c^\forall_{f,g}}

F-products and nonstandard hulls for semigroups

be the minimal number of uniform g-splitting trees needed to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. Let