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1994 | 145 | 2 | 101-119
Tytuł artykułu

On partitions of lines and space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a set, L, of lines in $ℝ^n$ and a partition of L into some number of sets: $L = L_1∪...∪ L_p$. We seek a corresponding partition $ℝ^n = S_1 ∪...∪ S_p$ such that each line l in $L_i$ meets the set $S_i$ in a set whose cardinality has some fixed bound, $ω_τ$. We determine equivalences between the bounds on the size of the continuum, $2^ω ≤ ω_θ$, and some relationships between p, $ω_τ$ and $ω_θ$.
Słowa kluczowe
Rocznik
Tom
145
Numer
2
Strony
101-119
Opis fizyczny
Daty
wydano
1994
otrzymano
1992-06-29
poprawiono
1993-12-16
poprawiono
1994-03-14
Twórcy
autor
  • Mathematical Institute, Hungarian Academy of Sciences, Reáltanoda U. 13-15, H-1053 Budapest, Hungary
  • Department of Mathematics, University of North Texas, Denton, Texas 76203, U.S.A., mauldin@unt.edu
Bibliografia
  • [B] F. Bagemihl, A proposition of elementary plane geometry that implies the continuum hypothesis, Z. Math. Logik Grundlag. Math. 7 (1961), 77-79.
  • [BH] G. Bergman and E. Hrushovski, Identities of cofinal sublattices, Order 2 (1985), 173-191.
  • [D1] R. Davies, On a problem of Erdős concerning decompositions of the plane, Proc. Cambridge Philos. Soc. 59 (1963), 33-36.
  • [D2] R. Davies, On a denumerable partition problem of Erdős, ibid., 501-502.
  • [Er] P. Erdős, Some remarks on set theory. IV, Michigan Math. J. 2 (1953-54), 169-173.
  • [EGH] P. Erdős, F. Galvin and A. Hajnal, On set-systems having large chromatic number and not containing prescribed subsystems, in: Infinite and Finite Sets (Colloq., Keszthely; dedicated to P. Erdős on his 60th birthday, 1973), Colloq. Math. Soc. János Bolyai 10, North-Holland, Amsterdam, 1975, 425-513.
  • [EH] P. Erdős and A. Hajnal, On chromatic number of graphs and set-systems, Acta. Math. Acad. Sci. Hungar. 17 (1966), 61-99.
  • [GG] F. Galvin and G. Gruenhage, A geometric equivalent of the continuum hypothesis, unpublished manuscript.
  • [J1] S. Jackson, A new proof of the strong partition relation on $ω_1$, Trans. Amer. Math. Soc. 320 (1990), 737-745.
  • [J2] S. Jackson, A computation of $δ^1_5$, to appear.
  • [Ku] C. Kuratowski, Sur une caractérisation des alephs, Fund. Math. 38 (1951), 14-17.
  • [S1] W. Sierpiński, Sur quelques propositions concernant la puissance du continu, ibid., 1-13.
  • [S2] W. Sierpiński, Hypothèse du continu, Warszawa, 1934.
  • [Si] R. Sikorski, A characterization of alephs, Fund. Math. 38 (1951), 18-22.
  • [Sm1] J. Simms, Sierpiński's theorem, Simon Stevin 65 (1991), 69-163.
  • [Sm2] J. Simms, Is $2^ω$ weakly inaccessible?, to appear.
  • [To] S. Todorčević, Partitioning pairs of countable ordinals, Acta Math. 159 (1987), 261-294.
  • [W] W. H. Woodin, Some consistency results in ZFC using AD, in: Cabal Seminar 79-81, Lecture Notes in Math. 1019, Springer, 1983, 172-198.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv145i2p101bwm
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