Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-25T03:44:00.336Z Has data issue: false hasContentIssue false
  • English
  • Français

An ordinal partition avoiding pentagrams

Published online by Cambridge University Press:  12 March 2014

Jean A. Larson
Jean A. Larson*
Affiliation:
Department of Mathematics, University of Florida, Po Box 118105, Gainesville, Fl 32611-8105, USA E-mail: jal@math.ufl.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Suppose that α = γ + δ where γ ≥ δ > 0. Then there is a graph which has no independent set of order type and has no pentagram (a pentagram is a set of five points with all pairs joined by edges). In the notation of Erdős and Rado. who generalized Ramsey's Theorem to this setting.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 3 , September 2000 , pp. 969 - 978
Copyright
Copyright © Association for Symbolic Logic 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Baumgartner, J., Remarks on partition relations for ω1, Set theory audits applications (Toronto, ON, 1987) (Steprans, J. and Watson, W. Stephen, editors), Lecture Notes in Mathematics, vol. 1401, Springer, 1989, pp. 5–17.Google Scholar
[2]Chang, C.C., A partition theorem for the complete graph on ωω, Journal of Combinatorial Theory, ser. A, vol. 12 (1972), pp. 396–452.CrossRefGoogle Scholar
[3]Darby, C., private communication.Google Scholar
[4]Darby, C., Negative partition relations for ordinals , Journal of Combinatorial Theory, Ser. B, vol. 76 (1999), pp. 205–222.CrossRefGoogle Scholar
[5]Darby, C. and Larson, J., A positive partition relationfor a critical countable ordinal, in preparation.Google Scholar
[6]Erdős, P., Some problems on finite and infinite graphs, Logic and combinatorics (Areata, CA, 1985) (Simpson, S., editor), Contemporary Mathematics, vol. 65, American Mathematical Society, 1987, pp. 223–228.Google Scholar
[7]Erdős, P. and Hajnal, A., Unsolved problems in set theory, Axiomatic set theory (University of California, Los Angeles, CA, 1967) (Scott, D.S., editor), Proceedings of Symposia in Pure Mathematematics, vol. 13, no. I, American Mathematical Society, Providence, RI, 1971, pp. 17–48.Google Scholar
[8]Erdős, P. and Milner, E.C., A theorem in the partition calculus, Canadian Mathematical Bulletin, vol. 15 (1972), pp. 501–505, Corrigendum, P. Erdős and E.C. Milner, A theorem in the partition calculus, Canadian Mathematical Bulletin, vol. 17 (1974) 305.CrossRefGoogle Scholar
[9]Galvin, F., Circulated lecture notes, University of Colorado, 1971.Google Scholar
[10]Galvin, F. and Larson, J., Pinning countable ordinals, Fundamenta Mathematicae, vol. 82 (1975), pp. 357–361.CrossRefGoogle Scholar
[11]Larson, J., A partition relationfor the ordinal ωω, Annals of Mathematical Logic, vol. 6 (1973), pp. 129–145.CrossRefGoogle Scholar
[12]Milner, E.C., Some combinatorial problems in set theory, Ph.D. thesis, London, 1962.Google Scholar
[13]Ramsey, F.P., On a problem of formal logic, Proceedings of the London Mathematical Society 2, vol. 30 (1930), pp. 264–286.Google Scholar
[14]Schipperus, R., Countable partition ordinals, Ph.D. thesis, University of Colorado, Boulder, 1999.Google Scholar
[15]Specker, E., Teilmengen von Mengen mil Relationen, Comment. Math. Helv., vol. 31 (1957), pp. 302–314.Google Scholar
[16]Williams, Neil, Combinatorial set theory, North Holland, Amsterdam, 1977.Google Scholar