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Title: | On cardinal sequences of length less than omega3 |
Author: | Martínez Alonso, Juan Carlos Soukup, Lajos |
Keywords: | Nombres cardinals Teoria de conjunts Àlgebra de Boole Dispersió (Matemàtica) Cardinal numbers Set theory Boolean algebras Scattering (Mathematics) |
Issue Date: | 15-Jun-2019 |
Publisher: | Elsevier B.V. |
Abstract: | We prove the following consistency result for cardinal sequences of length $<\omega_3$ : if GCH holds and $\lambda \geq \omega_2$ is a regular cardinal, then in some cardinal-preserving generic extension $2^\omega=\lambda$ and for every ordinal $\eta<\omega_3$ and every sequence $f=\left\langle\kappa_\alpha: \alpha<\eta\right\rangle$ of infinite cardinals with $\kappa_\alpha \leq \lambda$ for $\alpha<\eta$ and $\kappa_\alpha=\omega$ if $\operatorname{cf}(\alpha)=\omega_2$, we have that $f$ is the cardinal sequence of some LCS space. Also, we prove that for every specific uncountable cardinal $\lambda$ it is relatively consistent with ZFC that for every $\alpha, \beta<\omega_3$ with $\operatorname{cf}(\alpha)<\omega_2$ there is an LCS space $Z$ such that $\left.\operatorname{CS}(Z)=\langle\omega\rangle_\alpha \gamma \lambda\right\rangle_\beta$. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.topol.2019.04.002 |
It is part of: | Topology and its Applications, 2019, vol. 260, p. 116-125 |
URI: | https://hdl.handle.net/2445/193559 |
Related resource: | https://doi.org/10.1016/j.topol.2019.04.002 |
ISSN: | 0166-8641 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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