Primitive recursive bounds for van der Waerden numbers
Author:
Saharon Shelah
Journal:
J. Amer. Math. Soc. 1 (1988), 683-697
MSC:
Primary 05A17; Secondary 03D20
DOI:
https://doi.org/10.1090/S0894-0347-1988-0929498-X
MathSciNet review:
929498
Full-text PDF
References | Similar Articles | Additional Information
- [1] W. Ackermann, Zum Hilbertschen Aufbau der reelen Zahlen, Math. Ann. 99 (1928), 118-133. MR 1512441
- [2] E. R. Berlekamp, A construction for partitions which avoid long arithmetic progressions, Canad. Math. Bull. 11 (1968), 409-414. MR 0232743 (38:1066)
- [3] P. Erdös and R. Rado, Combinatorial theorems on classification of subsets of a given set, Proc. London Math. Soc. 2 (1952), 417-439. MR 0065615 (16:455d)
- [4] H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton Univ. Press, Princeton, N.J., 1982. MR 603625 (82j:28010)
- [5] R. L. Graham, K. Leeb, and B. L. Rothschild, Ramsey's theorem for a class of categories, Adv. in Math. 8 (1972), 417-433. MR 0306010 (46:5137b)
- [6] R. L. Graham and V. Rödl, Numbers in Ramsey theory, Surveys in Combinatorics 1987, London Math. Soc. Lecture Notes 123 (1987), 111-153. MR 905278 (89b:05125)
- [7]
R. L. Graham and B. L. Rothschild, Ramsey's theorem for
-parameter sets, Trans. Amer. Math. Soc. 159 (1971), 257-292. MR 0284352 (44:1580)
- [8] R. L. Graham, B. L. Rothschild, and J. H. Spencer, Ramsey theory, Wiley-Interscience Ser. in Discrete Math., New York, 1980. MR 591457 (82b:05001)
- [9] A. W. Hales and R. I. Jewett, Regularity and positional games, Trans. Amer. Math. Soc. 106 (1963), 222-229. MR 0143712 (26:1265)
- [10] J. Ketonen and R. Solovay, Rapidly growing Ramsey functions, Ann. of Math. 113 (1981), 267-314. MR 607894 (84c:03100)
- [11] H. E. Rose, Subrecursion: functions and hierarchies, Oxford Logic Guides 9, Oxford Univ. Press, Oxford, 1984. MR 752696 (86g:03004)
- [12] K. Roth, On certain sets of integers, J. London Math. Soc. 28 (1953), 104-109. MR 0051853 (14:536g)
- [13] J. H. Spencer, Ramsey's theorem for spaces, Trans. Amer. Math. Soc. 249 (1979), 363-371. MR 525678 (80d:05008)
- [14]
E. Szemerédi, On sets of integers containing no
elements in arithmetic progression, Acta Arith. 27 (1975), 199-245. MR 0369312 (51:5547)
- [15] B. L. van der Waerden, Beweis einer Baudetschen Vermutung, Nieuw Arch. Wisk. 15 (1927), 212-216.
- [16] B. Voigt, The partition problem for finite abelian groups, J. Comb. Theory Ser. A. 28 (1980), 257-271. MR 570208 (81h:05016)
Retrieve articles in Journal of the American Mathematical Society with MSC: 05A17, 03D20
Retrieve articles in all journals with MSC: 05A17, 03D20
Additional Information
DOI:
https://doi.org/10.1090/S0894-0347-1988-0929498-X
Keywords:
van der Waerden theorem,
Hales-Jewett theorem,
Graham-Rothschild theorem,
Ramsey theory,
primitive recursive functions
Article copyright:
© Copyright 1988
American Mathematical Society