5 citations · 11 across the 5 of their papers we have counts for
4 papers · 1 filter
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…
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.
Compact Sets of Baire Class One Functions and Maximal Almost Disjoint Families
Haim Horowitz, Stevo Todorcevic
We provide a proof that analytic almost disjoint families of infinite sets of integers cannot be maximal using a result of Bourgain about compact sets of Baire class one functions.…
Transcendence bases, well-orderings of the reals and the axiom of choice
Haim Horowitz, Saharon Shelah
We prove that there exists a transcendence basis for the realsthere is no well-ordering of the reals is consistent relative to . This answers a question of La…