All creatures great and small
Martin Goldstern, Saharon Shelah

TL;DR
This paper investigates the structure of clone lattices on large sets, showing that under certain set-theoretic assumptions, these lattices are not dually atomic, revealing complex properties of algebraic clones.
Contribution
It demonstrates that the clone lattice on a set of uncountable regular cardinal size is not dually atomic under specific set-theoretic conditions.
Findings
Clone lattice on a set of size kappa is not dually atomic.
Results depend on the assumption 2^kappa=kappa^+.
Provides insights into the structure of algebraic clones on large sets.
Abstract
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.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Logic, programming, and type systems
