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Generic graph construction
Journal of Symbolic Logic 49 (1):234-240 (1984)
Abstract
It is shown that if ZF is consistent, then so is ZFC + GCH + "There is a graph with cardinality ℵ 2 and chromatic number ℵ 2 such that every subgraph of cardinality ≤ ℵ 1 has chromatic number ≤ ℵ 0 ". This partially answers a question of Erdos and HajnalLinks
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Citations of this work
In memoriam: James Earl Baumgartner (1943–2011).J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7):877-909.
The Journal of Symbolic Logic. [REVIEW]Péter Komjáth - 2001 - Bulletin of Symbolic Logic 7 (4):539-541.
James E. Baumgartner. Generic graph construction. The journal of symbolic logic, vol. 49 , pp. 234–240. - Matthew Foreman and Richard Laver. Some downwards transfer properties for ℵ2. Advances in mathematics, vol. 67 , pp. 230–238. - Saharon Shelah. Incompactness for chromatic numbers of graphs. A tribute to Paul Erdős, edited by A. Baker, B. Bollobas, and A. Hajnal, Cambridge University Press, Cambridge, New York, and Oakleigh, Victoria, 1990, pp. 361–371. [REVIEW]Péter Komjáth - 2001 - Bulletin of Symbolic Logic 7 (4):539-541.
Review: James E. Baumgartner, Generic Graph Construction; Matthew Foreman, Richard Laver, Some Downwards Transfer Properties for $mathscr{N}_2$; Saharon Shelah, A. Baker, B. Bollobas, A. Hajnal, Incompactness for Chromatic Numbers of Graphs. [REVIEW]Péter Komjáth - 2001 - Bulletin of Symbolic Logic 7 (4):539-541.
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