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)

@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}
}