Splitting Number at Uncountable Cardinals

Zapletal, Jindrich

J. Symbolic Logic, Tome 62 (1997) no. 1, p. 35-42 / Harvested from Project Euclid

Résumé

We study a generalization of the splitting number $\mathfrak{s}$ to uncountable cardinals. We prove that $\mathfrak{s}(\kappa) > \kappa^+$ for a regular uncountable cardinal $\kappa$ implies the existence of inner models with measurables of high Mitchell order. We prove that the assumption $\mathfrak{s}(\aleph_\omega) > \aleph_{\omega + 1}$ has a considerable large cardinal strength as well.

Publié le : 1997-03-14
Classification:

@article{1183745183,
     author = {Zapletal, Jindrich},
     title = {Splitting Number at Uncountable Cardinals},
     journal = {J. Symbolic Logic},
     volume = {62},
     number = {1},
     year = {1997},
     pages = { 35-42},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745183}
}

Zapletal, Jindrich. Splitting Number at Uncountable Cardinals. J. Symbolic Logic, Tome 62 (1997) no. 1, pp.  35-42. http://gdmltest.u-ga.fr/item/1183745183/