8 papers · 1 filter
Splendid extensions
Shimon Garti
Let be a successor cardinal. We force a universe in which every model of PA of size extends to a model M of the same size, where M has no splendid extensions. If there is…
On a problem of Erdos and Hajnal
Shimon Garti, Yair Hayut, Saharon Shelah
We address a question of ErdÅs and Hajnal about the ordinary partition relation . For , assuming…
Length and ultraproducts
Shimon Garti, Saharon Shelah
We construct, in ZFC, a sequence of Boolean algebras for which the product of Lengths is strictly smaller than the Length of the product algebra.
Magidor-like forcing and the cofinality of the Galvin number
Shimon Garti
We force over a model of AD to obtain the consistency of the Galvin number having countable cofinality.
Echeloned saturation and forcing axioms
Shimon Garti
Addressing a question of Paul Larson we prove the following statement. If Chang's conjecture fails, Martin's axiom holds and the continuum is greater than , there are no…
Jonsson and Magidor filters
Omer Ben-Neria, Shimon Garti
We study the filter versions of square bracket partition relations, focusing on Jonssonicity and Magidority. We show that the singular cardinals in a Kleinberg sequence above some…