324 citations · 488 across the 179 of their papers we have counts for
7 papers · 2 filters
Free groups and automorphism groups of infinite fields
Philipp Lücke, Saharon Shelah
Let λbe a cardinal with λ=λ^{\aleph_0} and p be either 0 or a prime number. We show that there are fields K_0 and K_1 of cardinality λand characteristic p such that the automorphis…
Independent families in Boolean algebras with some separation properties
Piotr Koszmider, Saharon Shelah
We prove that any Boolean algebra with the subsequential completeness property contains an independent family of size continuum. This improves a result of Argyros from the 80ties w…
Saturating the random graph with an independent family of small range
M. Malliaris, S. Shelah
Motivated by Keisler's order, a far-reaching program of understanding basic model-theoretic structure through the lens of regular ultrapowers, we prove that for a class of regular…
Model-theoretic properties of ultrafilters built by independent families of functions
M. Malliaris, S. Shelah
Our results in this paper increase the model-theoretic precision of a widely used method for building ultrafilters, and so advance the general problem of constructing ultrafilters…
A Dividing Line Within Simple Unstable Theories
M. Malliaris, S. Shelah
We give the first (ZFC) dividing line in Keisler's order among the unstable theories, specifically among the simple unstable theories. That is, for any infinite cardinal for wh…
Perpendicular Indiscernible Sequences in Real Closed Fields
Eyal Firstenberg, Saharon Shelah
We investigate the behaviour of concepts from dependent theories when applied to real closed fields. Our main focus is on the concept of perpendicular indiscernible sequences, a co…