11 papers
Hereditarily separable groups and monochromatic uniformization
Paul C. Eklof, Alan H. Mekler, Saharon Shelah
We give a combinatorial equivalent to the existence of a non-free hereditarily separable group of cardinality aleph_1. This can be used, together with a known combinatorial equival…
On the p-rank of Ext
Alan H. Mekler, Andrzej Rosłanowski, Saharon Shelah
Assume V=L and lambda is regular smaller than the first weakly compact cardinal. Under those circumstances and with arbitrary requirements on the structure of Ext(G,Z) (under well…
The essentially free spectrum of a variety
Alan H. Mekler, Saharon Shelah, Otmar Spinas
We partially prove a conjecture from [MkSh:366] which says that the spectrum of almost free, essentially free, non-free algebras in a variety is either empty or consists of the cla…
Almost free algebras
Alan H. Mekler, Saharon Shelah
The essentially non-free spectrum is the class of uncountable cardinals kappa in which there is an essentially non-free algebra of cardinality kappa which is almost free. In L, the…
On coherent systems of projections for aleph_1 separable groups
Paul C. Eklof, Alan H. Mekler, Saharon Shelah
It is proved consistent with either CH or the negation of CH that there is an aleph_1-separable group of cardinality aleph_1 which does not have a coherent system of projections. I…
The canary tree
Alan H. Mekler, Saharon Shelah
A canary tree is a tree of cardinality the continuum which has no uncountable branch, but gains a branch whenever a stationary set is destroyed (without adding reals). Canary trees…