20 citations · 173 across the 54 of their papers we have counts for
54 papers
Quadruples and cubes
Shimon Garti
We prove, in , that the -terraced cube relation fails whenever is an uncountable cardinal. The corresponding terraced relation for quadruples fails for every $…
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 a…
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.
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…
On a problem of Erdos and Hajnal
Shimon Garti, Yair Hayut, Saharon Shelah
We address a question of Erdős and Hajnal about the ordinary partition relation . For , assuming $2^λ=λ…
Weak diamond and pcf theory
Shimon Garti
We obtain bounds on the cardinality of from instances of weak diamond. Consequently, under mild assumptions there are many singular cardinals of the from $\alep…