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
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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}
}