## Abstract

Let b denote the unboundedness number of ω^{ω}. That is, b is the smallest cardinality of a subset F ⊆ ω^{ω} such that for every g ∈ ω^{ω} there is f ∈ F such that {n: g(n) ≤ f(n)} is infinite. A Boolean algebra B is well-generated, if it has a well-founded sublattice L such that L generates B. We show that it is consistent with ZFC that א_{1} < 2^{א0} = b, and there is a Boolean algebra B such that B is not well-generated, and B is superatomic with cardinal sequence 〈א_{0}, א_{1}, א_{1}, 1〉. This result is motivated by the fact that if the cardinal sequence of a Boolean algebra B is 〈א_{0}, א_{0}, λ, 1〉, and B is not well-generated, then λ ≥ b.

Original language | English |
---|---|

Pages (from-to) | 221-239 |

Number of pages | 19 |

Journal | Israel Journal of Mathematics |

Volume | 123 |

DOIs | |

State | Published - 1 Jan 2001 |

## ASJC Scopus subject areas

- General Mathematics