324 citations · 1.7k across the 753 of their papers we have counts for
10 papers · 1 filter
Depth^+ and Length^+ of Boolean algebras
Shimon Garti, Saharon Shelah
Let inv denote the cardinal invariants Depth^+ and Length^+ on Boolean algebras. For many singular cardinals we create a strict inequality between the product of the inv values and…
A closed algebra with a non-Borel clone and an ideal with a Borel clone
Martin Goldstern, Michael Pinsker, Saharon Shelah
Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has on…
Clones above the unary clone
Martin Goldstern, Gábor Sági, Saharon Shelah
Let c be the cardinality of the continuum. We give a family of pairwise incomparable clones (on a countable base set) 2^c members, all with the same unary fragment, namely the set…
Universality of the lattice of transformation monoids
Michael Pinsker, Saharon Shelah
The set of all transformation monoids on a fixed set of infinite cardinality λ, equipped with the order of inclusion, forms a complete algebraic lattice Mon(λ) with 2^λ compact ele…
All creatures great and small
Martin Goldstern, Saharon Shelah
Let kappa be an uncountable regular cardinal. Assuming 2^kappa=kappa^+, we show that the clone lattice on a set of size kappa is not dually atomic.
Clones from Creatures
Martin Goldstern, Saharon Shelah
A clone on a set X is a set of finitary operations on X which contains all the projections and is closed under composition. The set of all clones forms a complete lattice Cl(X) wit…