324 citations · 1.7k across the 753 of their papers we have counts for
16 papers · 2 filters
A Borel maximal cofinitary group
Haim Horowitz, Saharon Shelah
We construct a Borel maximal cofinitary group.
On the classification of definable ccc forcing notions
Mohammad Golshani, Haim Horowitz, Saharon Shelah
We show that for a Suslin ccc forcing notion adding a Hechler real, ``all sets of reals are -measurable'' implies th…
Saccharinity with ccc
Haim Horowitz, Saharon Shelah
Using creature technology, we construct families of Suslin ccc non-sweet forcing notions such that is equiconsistent with "every set of reals equals a Borel…
Solovay's inaccessible over a weak set theory without choice
Haim Horowitz, Saharon Shelah
We study the consistency strength of Lebesgue measurability for sets over Zermelo set theory () in a completely choiceless context. We establish a result analogous to th…
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…
Maximal independent sets in Borel graphs and large cardinals
Haim Horowitz, Saharon Shelah
We construct a Borel graph G such that ZF+DC+"There are no maximal independent sets in G" is equiconsistent with ZFC+"There exists an inaccessible cardinal".