Geodesic
Separating Points and Coloring Principles
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 398-404

Voir la notice de l'article provenant de la source Cambridge University Press

In the mid 1970's, Shelah formulated a weak version of ◊. This axiom Φ is a prediction principle for colorings of the binary tree of height ω1. Shelah and Devlin showed that Φ is equivalent to 2א0 < 2א1 .In this paper, we formulate Φp, a "Φ for partial colorings", show that both ◊* and Fleissner's “◊ for stationary systems” imply Φp, that ◊ does not imply Φp and that Φp does not imply CH.We show that Φp implies that, in a normal first countable space, a discrete family of points of cardinality א1 is separated.
DOI : 10.4153/CMB-1984-061-3
Mots-clés : 03E05, 54D15, 54A35, 03E35, 03E45 
Watson, W. Stephen. Separating Points and Coloring Principles. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 398-404. doi: 10.4153/CMB-1984-061-3
@article{10_4153_CMB_1984_061_3,
     author = {Watson, W. Stephen},
     title = {Separating {Points} and {Coloring} {Principles}},
     journal = {Canadian mathematical bulletin},
     pages = {398--404},
     year = {1984},
     volume = {27},
     number = {4},
     doi = {10.4153/CMB-1984-061-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-061-3/}
}
TY  - JOUR
AU  - Watson, W. Stephen
TI  - Separating Points and Coloring Principles
JO  - Canadian mathematical bulletin
PY  - 1984
SP  - 398
EP  - 404
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-061-3/
DO  - 10.4153/CMB-1984-061-3
ID  - 10_4153_CMB_1984_061_3
ER  - 
%0 Journal Article
%A Watson, W. Stephen
%T Separating Points and Coloring Principles
%J Canadian mathematical bulletin
%D 1984
%P 398-404
%V 27
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-061-3/
%R 10.4153/CMB-1984-061-3
%F 10_4153_CMB_1984_061_3

[1] 1. Devlin, K. and Shelah, S., A weak version of ◊ which follows from 2ℵ0 &lt; 2ℵ1 , Israel Journal of Math 29 (1978) 239-247. Google Scholar | DOI

[2] 2. Fleissner, W. G., Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974) 294-298. Google Scholar | DOI

[3] 3. Mathias, A. R. D., Logic Colloquium 76, North Holland 1977, p. 542. Google Scholar

[4] 4. Shelah, S., S. A Note in General Topology; If then any normal space is ℵ-CWH; Preprints in Math. Logic, spring 1979. Google Scholar

[5] 5. Shelah, S., Whitehead Groups may not be free, even assuming CH, Israel Journal of Math. I 28 (1977) 193-204; II 35 (1980) 257–285. Google Scholar | DOI

[6] 6. Taylor, A. D., Diamond Principles, Ideals and the Normal Moore Space Problem. Can. Jour. Math. 33 (1981) 282-296. Google Scholar | DOI

Cité par Sources :