Laver Trees in the Generalized Baire Space

Yurii Khomskii, Marlene Koelbing, Giorgio Laguzzi +1

We prove that any suitable generalization of Laver forcing to the space ${\kappa }^{\kappa }$, for uncountable regular $\kappa$, necessarily adds a Cohen $\kappa$-real. We also study a dichotomy and an ide…