TY - JOUR
T1 - A note on δ-strongly compact cardinals
AU - Usuba, Toshimichi
N1 - Funding Information:
The author would like to thank the referee for many corrections and valuable comments. This research was supported by JSPS KAKENHI Grant Nos. 18K03403 and 18K03404 .
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/9/1
Y1 - 2021/9/1
N2 - In this paper we investigate more characterizations and applications of δ-strongly compact cardinals. We show that, for a cardinal κ, the following are equivalent: (1) κ is δ-strongly compact, (2) For every regular λ≥κ there is a δ-complete uniform ultrafilter over λ, and (3) Every product space of δ-Lindelöf spaces is κ-Lindelöf. We also prove that in the Cohen forcing extension, the least ω1-strongly compact cardinal is an exact upper bound on the tightness of the products of two countably tight spaces.
AB - In this paper we investigate more characterizations and applications of δ-strongly compact cardinals. We show that, for a cardinal κ, the following are equivalent: (1) κ is δ-strongly compact, (2) For every regular λ≥κ there is a δ-complete uniform ultrafilter over λ, and (3) Every product space of δ-Lindelöf spaces is κ-Lindelöf. We also prove that in the Cohen forcing extension, the least ω1-strongly compact cardinal is an exact upper bound on the tightness of the products of two countably tight spaces.
KW - Countably tight
KW - Lindelöf space
KW - Uniform ultrafilter
KW - δ-Strongly compact cardinal
KW - ω-Strongly compact cardinal
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U2 - 10.1016/j.topol.2020.107538
DO - 10.1016/j.topol.2020.107538
M3 - Article
AN - SCOPUS:85098139910
SN - 0166-8641
VL - 301
JO - Topology and its Applications
JF - Topology and its Applications
M1 - 107538
ER -