802 citations
- Heidelberg UniversityDE8 papers
- Centre National de la Recherche ScientifiqueFR6 papers
- Clausthal University of TechnologyDE4 papers
- University of Science and Technology of ChinaCN4 papers
- University of ViennaAT4 papers
- Hebrew University of JerusalemIL3 papers
- Yale UniversityUS3 papers
- Astronomical Institute of the Slovak Academy of SciencesSK2 papers
- Ben-Gurion University of the NegevIL2 papers
- College of Staten IslandUS2 papers
- ETH ZurichCH2 papers
- European Organization for Nuclear ResearchCH2 papers
8 papers · 1 filter
Ideal clones: Solution to a problem of Czedli and Heindorf
Martin Goldstern, Michael Pinsker
Given an infinite set X and an ideal I of subsets of X, the set of all finitary operations on X which map all (powers of) I-small sets to I-small sets is a clone. In a 2001 article…
A survey of clones on infinite sets
Martin Goldstern, Michael Pinsker
A clone on a set X is a set of finitary operations on X which contains all projections and which is moreover closed under functional composition. Ordering all clones on X by inclus…
Monoidal intervals of clones on infinite sets
Michael Pinsker
We show that for an infinite set X, if L is a completely distributive algebraic lattice with not more completely join irreducible elements than the size of the power set of X, then…
Precomplete clones on infinite sets which are closed under conjugation
Michael Pinsker
We show that on an infinite set, there exist no other precomplete clones closed under conjugation except those which contain all permutations. Since on base sets of some infinite c…
Clones containing all almost unary functions
Michael Pinsker
Let X be an infinite set of regular cardinality. We determine all clones on X which contain all almost unary functions. It turns out that independently of the size of X, these clon…
Maximal clones on uncountable sets that include all permutations
Michael Pinsker
We first determine the maximal clones on a set X of infinite regular cardinality which contain all permutations but not all unary functions, extending a result of Heindorf's for co…