324 citations · 1.7k across the 753 of their papers we have counts for
18 papers · 1 filter
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…
Borel completeness of some aleph_0 stable theories
Michael C. Laskowski, Saharon Shelah
We study aleph_0-stable theories, and prove that if T either has eni-DOP or is eni-deep, then its class of countable models is Borel complete. We introduce the notion of lambda-Bor…
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…