English

Hereditary Interval Algebras and Cardinal Characteristics of the Continuum

Logic 2023-03-13 v1

Abstract

An interval algebra is a Boolean algebra which is isomorphic to the algebra of finite unions of half-open intervals, of a linearly ordered set. An interval algebra is hereditary if every subalgebra is an interval algebra. We answer a question of M. Bekkali and S. Todor\v{c}evi\'c, by showing that it is consistent that every σ\sigma-centered interval algebra of size b\mathfrak{b} is hereditary. We also show that there is, in ZFC, an hereditary interval algebra of cardinality 1.\aleph_1.

Keywords

Cite

@article{arxiv.1905.13398,
  title  = {Hereditary Interval Algebras and Cardinal Characteristics of the Continuum},
  author = {Michael and Hrušák and Carlos and Martínez-Ranero and Ulises Ariet and Ramos-García},
  journal= {arXiv preprint arXiv:1905.13398},
  year   = {2023}
}