324 citations · 1.7k across the 753 of their papers we have counts for
12 papers · 2 filters
Turing Invariant Sets and the Perfect Set Property
Clovis Hamel, Haim Horowitz, Saharon Shelah
We show that "all Turing invariant sets of reals have the perfect set property" implies that all sets of reals have the perfect set property. We also show that this result…
Classification over a predicate -- the general case. Part I -- structure theory
Saharon Shelah, Alexander Usvyatsov
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier…
Colouring of successor of regular again
Saharon Shelah
We get a quite maximal version of the colouring property by proving when are regular cardinals.
Borel sets without perfectly many overlapping translations, II
Andrzej Roslanowski, Saharon Shelah
For a countable ordinal epsilon we construct a Sigma^0_2 subset of the Cantor space for which one may force aleph_epsilon translations with intersections of size 2i, but such that…
Infinite monochromatic paths and a theorem of Erdos-Hajnal-Rado
Shimon Garti, Menachem Magidor, Saharon Shelah
We prove that if and then .
On the non-existence of -mad families
Haim Horowitz, Saharon Shelah
Starting from a model with a Laver-indestructible supercompact cardinal , we construct a model of where there are no -mad families.