324 citations · 1.7k across the 753 of their papers we have counts for
813 papers
Kaplansky decompositions of Polish modules
Ivo Herzog, Gianluca Paolini, Saharon Shelah
Let be a countable ring. Given an -module , we call a decomposition a Kaplansky decomposition if each is countable. We characterize th…
Adding the constant evasion and constant prediction numbers to Cichoń's maximum
Miguel A. Cardona, Miroslav Repický, Saharon Shelah
Let be the constant evasion number, that is, the size of the least family of reals such that for each predictor $π\colon {}^{<ω}2\…
Forcing Diamond and Applications to Iterability
Heike Mildenberger, Saharon Shelah
We show that higher Sacks forcing at a regular limit cardinal and club Miller forcing at an uncountable regular cardinal both add a diamond sequence. We answer the longstanding que…
A permutation group acting transitively on certain collections of models
Samuel M. Corson, Saharon Shelah
It is shown, from -centered Martin's Axiom, that there exists a proper dense subgroup of the symmetric group on a countably infinite set whose natural action on sufficiently fle…
Quite free p-groups with trivial duality
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
We present a class of abelian groups that exhibit a high degree of freeness while possessing no non-trivial homomorphisms to a canonical free object. Unlike prior investigations, w…
An analogue of U-rank for atomic classes
John T. Baldwin, Michael C. Laskowski, Saharon Shelah
For a countable, complete, first-order theory , we study , the class of atomic models of . We develop an analogue of -rank and prove two results. On one hand, if some…