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An overview of the proof in "Borel Conjecture and Dual Borel Conjecture"
Martin Goldstern, Jakob Kellner, Saharon Shelah +1
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
A closed algebra with a non-Borel clone and an ideal with a Borel clone
Martin Goldstern, Michael Pinsker, Saharon Shelah
Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has on…
Partition Calculus and Cardinal Invariants
Shimon Garti, Saharon Shelah
We prove that the strong polarized relation of above applied simultaneously for every cardinal in the interval is consistent. We conclude that this posi…
Trivial automorphisms
Ilijas Farah, Saharon Shelah
We prove that the statement `For all Borel ideals I and J on , every isomorphism between Boolean algebras and has a continuous representation' is relatively co…
Nice aleph_1 generated non-P-points, I
Saharon Shelah
We define a family of a (non-principal) ultrafilters on N which are, in a sense, far from P-points. We first under reasonable conditions, prove its existence. In a continuation we…
Chain conditions in dependent groups
Itay Kaplan, Saharon Shelah
In this note we prove and disprove some chain conditions in type definable and definable groups in dependent, strongly dependent and strongly^{2} dependent theories.