00925njm 22002777a 4500
dc
Bagaria, Joan
author
da Silva, Samuel G.
author
2023-01-01
We present more applications of the recently introduced -strongly compact cardinals in the context of either consistency or reflection results in General Topology, focusing on issues related to normality. In particular, we show that such large cardinal notion provides a new upper bound for the consistency strength of the statement “All normal Moore spaces are metrizable” (NMSC). The proof uses random forcing, as in the original consistency proof of NMSC due to Nykos-Kunen-Solovay (see Fleissner [10]). We establish a compactness theorem for normality (i.e., reflection of non-normality) in the realm of first countable spaces, using the least -strongly compact cardinal, as well as two more similar compactness results on related topological properties. We finish the paper by combining the techniques of reflection and forcing to show that our new upper bound for the consistency strength of NMSC can be also obtained via Cohen forcing, using some arguments from Dow-Tall-Weiss.
0166-8641
http://hdl.handle.net/2445/214429
744329
$\omega_1$-strongly compact cardinals and normality