# Sh:E3

- Shelah, S. (1996).
*On some problems in general topology*. In Set theory (Boise, ID, 1992–1994), Vol. 192, Amer. Math. Soc., Providence, RI, pp. 91–101. arXiv: 0708.1981 DOI: 10.1090/conm/192/02352 MR: 1367138 -
Abstract:

We prove that Arhangelskii’s problem has a consistent positive answer: if V satisfies CH, then for some \aleph_1-complete \aleph_2-c.c. forcing notion P of cardinality \aleph_2 we have that P forces “CH and there is a Lindelof regular topological space of size \aleph_2 with clopen basis with every point of pseudo-character \aleph_0 (i.e. each singleton is the intersection of countably many open sets)”. Also, we prove the consistency of: CH+ 2^{\aleph_1} > \aleph_2 + "there is no space as above with \aleph_2 points" (starting with a weakly compact cardinal). - Version 2020-02-18 (11p) published version (11p)

Bib entry

@incollection{Sh:E3, author = {Shelah, Saharon}, title = {{On some problems in general topology}}, booktitle = {{Set theory (Boise, ID, 1992--1994)}}, series = {Contemp. Math.}, volume = {192}, year = {1996}, pages = {91--101}, publisher = {Amer. Math. Soc., Providence, RI}, mrnumber = {1367138}, mrclass = {03E35 (54A25 54D15)}, doi = {10.1090/conm/192/02352}, note = {\href{https://arxiv.org/abs/0708.1981}{arXiv: 0708.1981}}, arxiv_number = {0708.1981} }