Clones from Creatures
Martin Goldstern, Saharon Shelah
Abstract
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) with greatest element O, the set of all finitary operations. For finite sets X the lattice is "dually atomic": every clone other than O is below a coatom of Cl(X). It was open whether Cl(X) is also dually atomic for infinite X. Assuming the continuum hypothesis, we show that there is a clone C on a countable set such that the interval of clones above C is linearly ordered, uncountable, and has no coatoms.
Create a lesson
Related papers
Directed partial orders on the complex number field
Wenyi Wang, Ruisong Yuan, Yuehui Zhang et al.
Polynomial identities, central polynomials and cocharacters of M2(F) with G-graded involution
Rafael Bezerra dos Santos, Lucas Reis
Polynomial identities, central polynomials and cocharacters of M2(F) with transpose superinvolution
Rafael Bezerra dos Santos, Lucas Reis
Range-compatible homomorphisms on Hermitian matrices
Clément de Seguins Pazzis
Transposed Triple Products and Pro-Symmetric Rings in -Rings
Huaxi Chen, Long Wang, Honglin Zou
On -Reversible and Generalized -Reversible Rings
Huaxi Chen, Long Wang, Honglin Zou