Combinatorics for the dominating and unsplitting numbers
Aubrey, Jason
J. Symbolic Logic, Tome 69 (2004) no. 1, p. 482-498 / Harvested from Project Euclid
In this paper we introduce a new property of families of functions on the Baire space, called pseudo-dominating, and apply the properties of these families to the study of cardinal characteristics of the continuum. We show that the minimum cardinality of a pseudo-dominating family is min{𝖗, 𝖉}. We derive two corollaries from the proof: 𝖗 ≥ min{ 𝖉, 𝖚 } and min{ 𝖉, 𝖗 } = min{ 𝖉, 𝖗_σ }. We show that if a dominating family is partitioned into fewer that 𝖘 pieces, then one of the pieces is pseudo-dominating. We finally show that 𝖚 < 𝖌 implies that every unbounded family of functions is pseudo-dominating, and that the Filter Dichotomy principle is equivalent to every unbounded family of functions being finitely pseudo-dominating.
Publié le : 2004-06-15
Classification: 
@article{1082418539,
     author = {Aubrey, Jason},
     title = {Combinatorics for the dominating and unsplitting numbers},
     journal = {J. Symbolic Logic},
     volume = {69},
     number = {1},
     year = {2004},
     pages = { 482-498},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1082418539}
}
Aubrey, Jason. Combinatorics for the dominating and unsplitting numbers. J. Symbolic Logic, Tome 69 (2004) no. 1, pp.  482-498. http://gdmltest.u-ga.fr/item/1082418539/