324 citations · 1.7k across the 753 of their papers we have counts for
33 papers · 2 filters
Uniformization and Skolem functions in the class of trees
Shmuel Lifsches, Saharon Shelah
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T…
The cofinality spectrum of the infinite symmetric group
Saharon Shelah, Simon Thomas
A group G that is not finitely generated can be written as the union of a chain of proper subgroups. The cofinality spectrum of G, written CF(S), is the set of regular cardinals la…
The universality spectrum: Consistency for more classes
Saharon Shelah
We deal with consistency results for the existence of universal models in natural classes of models (more exactly--a somewhat weaker version). We apply a result on quite general fa…
Possible pcf algebras
Thomas Jech, Saharon Shelah
There exists a family of sets of countable ordinals such that o , o if then , o if and is a limit ordinal t…
On finite rigid structures
Yuri Gurevich, Saharon Shelah
The main result of this paper is a probabilistic construction of finite rigid structures. It yields a finitely axiomatizable class of finite rigid structures where no L^omega_{inft…
McColm conjecture
Yuri Gurevich, Neil Immerman, Saharon Shelah
Gregory McColm conjectured that positive elementary inductions are bounded in a class K of finite structures if every (FO + LFP) formula is equivalent to a first-order formula in K…