Eprints of Rényi Institute

A note on Noetherian type of spaces

Soukup, Lajos (2010) A note on Noetherian type of spaces. (Unpublished)



The Noetherian type of a space X, Nt(X), is the least cardinal \kappa such that X has a base B such that |\{b'\in B: b\subset b'\}|<\kappa for each b\in B. Denote by X the space obtained from 2^{\aleph_\omega} by declaring the G_\delta sets to be open. Milovich proved that if \square_{\aleph_\omega} holds and (\aleph_\omega)^\omega=\aleph_{\omega+1} then Nt(X)=\omega_1.
Answering a question of Spadaro, we show that if (\aleph_\omega)^\omega=\aleph_{\omega+1} and the Chang Conjecture holds for \aleph_{\omega}, then Nt(X)=\omega_2.

Item Type:Research Paper
Keywords and phrases:Noetherian type, Chang Conjecture, large cardinals, $G_\delta$ topology
Subjects:03E35 Consistency and independence results
Divisions:Research Divisions > Set theory and general topology
Last Modified:29 Mar 2010 15:20

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