20 citations · 173 across the 54 of their papers we have counts for
6 papers · 1 filter
Amenable colorings
Shimon Garti
Let be any regular cardinal. Assuming the existence of a huge cardinal above , we prove the consistency of for every ordinal $τ<…
Weak prediction principles
Omer Ben-Neria, Shimon Garti, Yair Hayut
We prove the consistency of the failure of the weak diamond at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond is equivalent to t…
How you are with and ?
Shimon Garti, Saharon Shelah
We prove that if there is a real-valued measurable cardinal then the splitting number is . Likewise, if the continuum is real-valued measurable then the reaping number eq…
Weak diamond and Galvin's property
Shimon Garti
We prove that the Devlin-Shelah weak diamond implies Galvin's property. On the other hand, Galvin's property is consistent with the negation of the weak diamond, and even with Mart…
On the spectrum of characters of ultrafilters
Shimon Garti, Menachem Magidor, Saharon Shelah
We show that the character spectrum , for a singular cardinal of countable cofinality, may include any prescribed set of regular cardinals between and .
On the verge of inconsistency: Magidor cardinals and Magidor filters
Shimon Garti, Yair Hayut, Saharon Shelah
We introduce a model-theoretic characterization of Magidor cardinals, from which we infer that Magidor filters are beyond ZFC-inconsistency