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DECIDING THE CHROMATIC NUMBERS OF ALGEBRAIC HYPERGRAPHS

Published online by Cambridge University Press:  01 May 2018

JAMES H. SCHMERL
JAMES H. SCHMERL*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CONNECTICUT STORRS, CT06269, USAE-mail:[email protected]
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Abstract

For each infinite cardinal κ, the set of algebraic hypergraphs having chromatic number no larger than κ is decidable.

Keywords

05C1505C63algebraic hypergraphschromatic number
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 128 - 145
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

REFERENCES

Baumgartner, J. E., Canonical partition relations, this Journal, 40 (1975), pp. 541–554.Google Scholar
Bochnak, J., Coste, M., and Roy, M.-F., Real Algebraic Geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 36, Springer-Verlag, Berlin, 1998.Google Scholar
Basu, S., Pollack, R., and Roy, M.-F., Algorithms in Real Algebraic Geometry, second ed., Algorithms and Computation in Mathematics, vol. 10, Springer-Verlag, Berlin, 2006.Google Scholar
Ceder, J., Finite subsets and countable decompositions of Euclidean spaces. Revue Roumaine de Mathématiques Pures et Appliquées, vol. 14 (1969), pp. 1247–1251.Google Scholar
Davies, R. O., Partitioning the plane into denumberably many sets without repeated distances. Proceedings of the Cambridge Philosophical Society, vol. 72 (1972), pp. 179–183.Google Scholar
Erdős, P. and Komjáth, P., Countable decompositions of R2 and R3. Discrete & Computational Geometry, vol. 5 (1990), pp. 325–331.CrossRefGoogle Scholar
Fox, J., An infinite color analogue of Rado’s theorem. Journal of Combinatorial Theory, Series A, vol. 114 (2007), pp. 1456–1469.Google Scholar
Komjáth, P., Tetrahedron free decomposition of R3. Bulletin of the London Mathematical Society, vol. 23 (1991), pp. 116–120.Google Scholar
Kunen, K., Partitioning Euclidean space. Mathematical Proceedings of the Cambridge Philosophical Society, vol. 102 (1987), pp. 379–383.CrossRefGoogle Scholar
Schmerl, J. H., Partitioning Euclidean space. Discrete & Computational Geometry, vol. 10 (1993), pp. 101–106.Google Scholar
Schmerl, J. H., Triangle-free partitions of Euclidean space. Bulletin of the London Mathematical Society, vol. 26 (1994), pp. 483–486.Google Scholar
Schmerl, J. H., Countable partitions of Euclidean space. Mathematical Proceedings of the Cambridge Philosophical Society, vol. 120 (1996), pp. 7–12.Google Scholar
Schmerl, J. H., Avoidable algebraic subsets of Euclidean space. Transactions of the American Mathematical Society, vol. 352 (2000), pp. 2479–2489.Google Scholar
Schmerl, J. H., Chromatic numbers of algebraic hypergraphs. Combinatorica (2016), pp. 1–16.Google Scholar
van den Dries, L, Algebraic theories with definable Skolem functions, this Journal, vol. 49 (1984), pp. 625–629.Google Scholar