3 papers
math.LO2020
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 , for uncountable regular , necessarily adds a Cohen -real. We also study a dichotomy and an ide…
math.LO2020
Bounded Symbiosis and Upwards Reflection
Lorenzo Galeotti, Yurii Khomskii, Jouko Väänänen
Bagaria and Väänänen developed a framework for studying the large cardinal strength of downwards Löwenheim-Skolem theorems and related set theoretic reflection properties. The main…
math.LO2019
Definable Maximal Independent Families
Jörg Brendle, Vera Fischer, Yurii Khomskii
We study maximal independent families (m.i.f.) in the projective hierarchy. We show that (a) the existence of a m.i.f. is equivalent to the existence of a $\bold…