2 citations · 3 across the 4 of their papers we have counts for
10 papers · 1 filter
Infinite Stable Graphs With Large Chromatic Number II
Yatir Halevi, Itay Kaplan, Saharon Shelah
We prove a version of the strong Taylor's conjecture for stable graphs: if is a stable graph whose chromatic number is strictly greater than then contai…
Infinite Stable Graphs With Large Chromatic Number
Yatir Halevi, Itay Kaplan, Saharon Shelah
We prove that if is an -stable (respectively, superstable) graph with (respectively, ) then contains all the finite subgraphs of the…
Criteria for exact saturation and singular compactness
Itay Kaplan, Nicholas Ramsey, Saharon Shelah
We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satis…
Non-forking and preservation of NIP and dp-rank
Pedro Andrés Estevan, Itay Kaplan
We investigate the question of whether the restriction of a NIP type which does not fork over to is also NIP, and the analogous question for dp-rank.…
On uniform definability of types over finite sets for NIP formulas
Shlomo Eshel, Itay Kaplan
Combining two results from machine learning theory we prove that a formula is NIP if and only if it satisfies uniform definability of types over finite sets (UDTFS). This settles a…
Transitivity of Kim-independence
Itay Kaplan, Nicholas Ramsey
We prove several results on the behavior of Kim-independence upon changing the base in NSOP theories. As a consequence, we prove that Kim-independence satisfies transitivity…