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Keywords:
small Dowker space; Dowker product; normality; countable paracompactness; measurable cardinal; Covering Lemma
small Dowker space; Dowker product; normality; countable paracompactness; measurable cardinal; Covering Lemma
Summary:
We prove that if there is a model of set-theory which contains no first countable, locally compact, scattered, countably paracompact space $X$, whose Tychonoff square is a Dowker space, then there is an inner model which contains a measurable cardinal.
References:
[B1] Bešlagić A.: A Dowker product. Trans. Amer. Math. Soc. 292 (1985), 519-530. MR 0808735
[B2] Bešlagić A.: Another Dowker product. Top. Appl. 36 (1990), 553-264. MR 1070704
[B3] Bešlagić A.: Yet another Dowker product. preprint. MR 1261168
[Dv] Devlin K.: Constructability. Springer Verlag Berlin (1984). MR 0750828
[DJ] Dodd A.J., Jensen R.: The covering lemma for K. Ann. Math. Logic 22 (1982), 1-30. MR 0661475 | Zbl 0492.03014
[Dk] Dowker C.H.: On countably paracompact spaces. Canad. J. Math. 3 (1951), 219-224. MR 0043446 | Zbl 0042.41007
[E] Engelking R.: General Topology. Heldermann Verlag Berlin (1989). MR 1039321 | Zbl 0684.54001
[F] Fleissner W.G.: The normal Moore space conjecture and large cardinals. {in: [KV]} 733-760. MR 0776635 | Zbl 0562.54039
[G] Good C.: Large cardinals and small Dowker spaces. to appear in Proc. Amer. Math. Soc. MR 1216813 | Zbl 0821.03025
[K] Kunen K.: Set Theory, An Introduction to Independence Proofs. North Holland Amsterdam (1984). MR 0756630
[KV] Kunen K., Vaughan J.E. eds.: Handbook of Set-Theoretic Topology. North Holland Amsterdam (1984). MR 0776619 | Zbl 0546.00022
[R] Rudin M.E.: Dowker spaces. in: [KV] 761-780. MR 0776636 | Zbl 0566.54009
[RS] Rudin M.E., Starbird M.: Products with a metric factor. Gen. Top. Appl. 5 1975 235-248. MR 0380709 | Zbl 0305.54010
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