# Sh:872

- Kellner, J., & Shelah, S. (2009).
*Decisive creatures and large continuum*. J. Symbolic Logic,**74**(1), 73–104. arXiv: math/0601083 DOI: 10.2178/jsl/1231082303 MR: 2499421 -
Abstract:

For f>g\in\omega^\omega let c^{\forall}_{f,g} be the minimal number of uniform trees with g-splitting needed to \forall^\infty-cover the uniform tree with f-splitting. c^{\exists}_{f,g} is the dual notion for the \exists^\infty-cover.Assuming CH and given \aleph_1 many (sufficiently different) pairs (f_\epsilon,g_\epsilon) and cardinals \kappa_\epsilon such that \kappa_\epsilon^{\aleph_0}=\kappa_\epsilon, we construct a partial order forcing that c^{\exists}_{f_\epsilon,g_\epsilon}= c^{\forall}_{f_\epsilon,g_\epsilon}=\kappa_\epsilon.

For this, we introduce a countable support semiproduct of decisive creatures with bigness and halving. This semiproduct satisfies fusion, pure decision and continuous reading of names.

- Version 2006-07-07_11 (18p) published version (33p)

Bib entry

@article{Sh:872, author = {Kellner, Jakob and Shelah, Saharon}, title = {{Decisive creatures and large continuum}}, journal = {J. Symbolic Logic}, fjournal = {The Journal of Symbolic Logic}, volume = {74}, number = {1}, year = {2009}, pages = {73--104}, issn = {0022-4812}, mrnumber = {2499421}, mrclass = {03E17 (03E40)}, doi = {10.2178/jsl/1231082303}, note = {\href{https://arxiv.org/abs/math/0601083}{arXiv: math/0601083}}, arxiv_number = {math/0601083} }