A consistency theorem for cardinal sequences of length $< \omega_3$

Juan Carlos Martínez; Lajos Soukup

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arXiv · 2512.01418

A consistency theorem for cardinal sequences of length $< \omega_3$

Juan Carlos Martínez·Lajos Soukup

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Abstract

We prove that if $\lambda$ is a fixed uncountable cardinal and $f = \langle \ka_{\al} : \al < \delta \rangle$ is a sequence of infinite cardinals where $\delta < \omega_3$ and $\ka_{\al}\in \{\om,\lambda\}$ for each $\al < \delta$ in such a way that $f^{-1}\{\om\}$ is $\om_2$-closed in $\delta$, then it is consistent that there is a scattered Boolean space whose cardinal sequence is $f$.

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BibTeX RIS

Juan Carlos Martínez, Lajos Soukup. 2025-12-01. A consistency theorem for cardinal sequences of length $< \omega_3$. https://arxiv.org/abs/2512.01418

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