1 citations · 1 across the 7 of their papers we have counts for
10 papers
Functional Projection and Complexity Reduction
Vera Fischer, Yurii Khomskii, Yipu Li +1
Törnquist (arXiv:1310.3250) proved that if there exists a maximal almost disjoint (MAD) family, then there exists a MAD family. Since then, se…
Combinatorial Properties of the Raisonnier Filter
Spyridon Dialiatsis, Yurii Khomskii
The Raisonnier Filter is a combinatorial object isolated by Jean Raisonnier in order to simplify Shelah's proof that if all sets are Lebesgue-measurable then the…
Paraconsistent and Paracomplete Zermelo-Fraenkel Set Theory
Yurii Khomskii, Hrafn Valtýr Oddsson
We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true…
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…
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…
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…
Filter-Laver Measurability
Yurii Khomskii
We study sigma-ideals and regularity properties related to the "filter-Laver" and "dual-filter-Laver" forcing partial orders. An important innovation which enables this study is a…
Cofinalities of Marczewski-like ideals
Joerg Brendle, Yurii Khomskii, Wolfgang Wohofsky
We show that the cofinalities of both the Miller ideal m^0 (the sigma-ideal naturally related to Miller forcing) and the Laver ideal ell^0 (related to Laver forcing) are larger tha…
Almost disjoint refinements and mixing reals
Barnabás Farkas, Yurii Khomskii, Zoltán Vidnyánszky
We investigate families of subsets of with almost disjoint refinements in the classical case as well as with respect to given ideals on . More precisely, we study the follow…
Regularity Properties on the Generalized Reals
Sy-David Friedman, Yurii Khomskii, Vadim Kulikov
We investigate regularity properties derived from tree-like forcing notions in the setting of "generalized descriptive set theory", i.e., descriptive set theory on and ,…