No CrossRef data available.
Article contents
PARTITION OF LARGE SUBSETS OF SEMIGROUPS
Published online by Cambridge University Press: 03 January 2024
Abstract
It is known that in an infinite very weakly cancellative semigroup with size $\kappa $, any central set can be partitioned into $\kappa $ central sets. Furthermore, if $\kappa $ contains $\lambda $ almost disjoint sets, then any central set contains $\lambda $ almost disjoint central sets. Similar results hold for thick sets, very thick sets and piecewise syndetic sets. In this article, we investigate three other notions of largeness: quasi-central sets, C-sets, and J-sets. We obtain that the statement applies for quasi-central sets. If the semigroup is commutative, then the statement holds for C-sets. Moreover, if $\kappa ^\omega = \kappa $, then the statement holds for J-sets.
MSC classification
- Type
- Article
- Information
- Copyright
- © The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic