Clones from ideals
Mathias Beiglb\"ock, Martin Goldstern, Lutz Heindorf, Michael, Pinsker
TL;DR
This paper explores the relationship between ideals of subsets of an infinite set and the corresponding clones of operations that preserve small sets, analyzing their position within the clone lattice.
Contribution
It extends previous work by examining the placement of clones derived from ideals within the clone lattice on infinite sets.
Findings
Characterization of clones associated with ideals on infinite sets
Analysis of the position of these clones in the clone lattice
Extension of earlier investigations on clone structure
Abstract
On an infinite base set X, every ideal of subsets of X can be associated with the clone of those operations on X which map small sets to small sets. We continue earlier investigations on the position of such clones in the clone lattice.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Algebra and Logic · Rings, Modules, and Algebras