Large cardinals and Dowker products

Chris Good

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 3, page 515-522
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Good, Chris. "Large cardinals and Dowker products." Commentationes Mathematicae Universitatis Carolinae 35.3 (1994): 515-522. <http://eudml.org/doc/247567>.

@article{Good1994,
abstract = {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.},
author = {Good, Chris},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {small Dowker space; Dowker product; normality; countable paracompactness; measurable cardinal; Covering Lemma; combinatorial principles; Dowker products; normality; countable paracompactness; Dowker space},
language = {eng},
number = {3},
pages = {515-522},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Large cardinals and Dowker products},
url = {http://eudml.org/doc/247567},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Good, Chris
TI - Large cardinals and Dowker products
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 3
SP - 515
EP - 522
AB - 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.
LA - eng
KW - small Dowker space; Dowker product; normality; countable paracompactness; measurable cardinal; Covering Lemma; combinatorial principles; Dowker products; normality; countable paracompactness; Dowker space
UR - http://eudml.org/doc/247567
ER -

References

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  1. Bešlagić A., A Dowker product, Trans. Amer. Math. Soc. 292 (1985), 519-530. (1985) MR0808735
  2. Bešlagić A., Another Dowker product, Top. Appl. 36 (1990), 553-264. (1990) MR1070704
  3. Bešlagić A., Yet another Dowker product, preprint. MR1261168
  4. Devlin K., Constructability, Springer Verlag Berlin (1984). (1984) MR0750828
  5. Dodd A.J., Jensen R., The covering lemma for K, Ann. Math. Logic 22 (1982), 1-30. (1982) Zbl0492.03014MR0661475
  6. Dowker C.H., On countably paracompact spaces, Canad. J. Math. 3 (1951), 219-224. (1951) Zbl0042.41007MR0043446
  7. Engelking R., General Topology, Heldermann Verlag Berlin (1989). (1989) Zbl0684.54001MR1039321
  8. Fleissner W.G., The normal Moore space conjecture and large cardinals, {in: [KV]} 733-760. Zbl0562.54039MR0776635
  9. Good C., Large cardinals and small Dowker spaces, to appear in Proc. Amer. Math. Soc. Zbl0821.03025MR1216813
  10. Kunen K., Set Theory, An Introduction to Independence Proofs, North Holland Amsterdam (1984). (1984) MR0756630
  11. Kunen K., Vaughan J.E. eds., Handbook of Set-Theoretic Topology, North Holland Amsterdam (1984). (1984) Zbl0546.00022MR0776619
  12. Rudin M.E., Dowker spaces, in: [KV] 761-780. Zbl0566.54009MR0776636
  13. Rudin M.E., Starbird M., Products with a metric factor, Gen. Top. Appl. 5 1975 235-248. (1975) Zbl0305.54010MR0380709

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