321 citations
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7 papers · 1 filter
Forcing, games and families of closed sets
Marcin Sabok
We propose a new, game-theoretic, approach to the idealized forcing, in terms of fusion games. This generalizes the classical approach to the Sacks and the Miller forcing. For defi…
On stable fields and weight
Krzysztof Krupinski, Anand Pillay
We prove that if K is an infinite stable field whose generic type has weight 1 then K is separably closed. We also obtain partial results when the generic of K has finite weight an…
Combinatorial geometries of field extensions
Jakub Gismatullin
We classify the algebraic combinatorial geometries of arbitrary field extensions of transcendence degree greater than 4 and describe their groups of automorphisms. Our results and…
Isometry types of profinite groups
Al. A. Ivanov
Let T be a rooted tree and Iso(T) be the group of isometries of T. Using model-theoretic tools we study closed subgroups G of Iso(T) with respect to the number of conjugacy classes…
Continuous functions taking every value a given number of times
Aleksandra Kwiatkowska
We give necessary and sufficient conditions on a function $f:[0,1]\to {0,1,2,...,ω,\continuum}$ under which there exists a continuous function such that for ever…
G-Compactness and Groups
Jakub Gismatullin, Ludomir Newelski
Lascar described E_KP as a composition of E_L and the topological closure of EL. We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to…