8 papers
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.
List chromatic numbers and singular compactness
Shimon Garti
We prove that the list chromatic number of graphs satisfies singular compactness at strong limit singular cardinals.
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…