5 papers
Strong subgroup chains and the Baer-Specker group
Oren Kolman
Examples are given of non-elementary properties that are preserved under C-filtrations for various classes C of Abelian groups. The Baer-Specker group is never the union of a chain…
Almost disjoint pure subgroups of the Baer-Specker group
Oren Kolman, Saharon Shelah
We prove in ZFC that the Baer-Specker group Z^omega has 2^{aleph_1} non-free pure subgroups of cardinality aleph_1 which are almost disjoint: there is no non-free subgroup embeddab…
Infinitary Axiomatizability of Slender and Cotorsion-Free Groups
Oren Kolman, Saharon Shelah
The classes of slender and cotorsion-free abelian groups are axiomatizable in the infinitary logics L_{infty,omega_1} and L_{infty,omega}, respectively. The Baer-Specker group Z^om…
A result related to the problem CN of Fremlin
Oren Kolman, Saharon Shelah
We show that the set of injective functions from any uncountable cardinal less than the continuum into the real numbers is of second category in the box product topology.
Categoricity and amalgamation for AEC and measurable
Oren Kolman, Saharon Shelah
In the original version of this paper, we assume a theory that the logic is categorical in a cardinal , and is a measurable cardinal. Ther…