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Kolmogorov complexity and symmetric relational structures

Published online by Cambridge University Press:  12 March 2014

W. L. Fouché  and
P. H. Potgieter
W. L. Fouché
Affiliation:
Department of Mathematics and Applied Mathematics, University of Pretoria, 0002 Pretoria, South Africa E-mail: [email protected]
P. H. Potgieter
Affiliation:
Department of Quantitative Management, University of South Africa, Po Box 392, 0003 Pretoria, South Africa E-mail: [email protected]
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Abstract

We study partitions of Fraïssé limits of classes of finite relational structures where the partitions are encoded by infinite binary strings which are random in the sense of Kolmogorov-Chaitin.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 1083 - 1094
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1]Brightwell, G., Prömel, H. J., and Steger, A., The average number of linear extensions of a partial order, Journal of Combinatorial Theory, Series A, vol. 73 (1996), pp. 193–206.CrossRefGoogle Scholar
[2]Chaitin, G. J., Algorithmic information theory, Cambridge University Press, 1987.CrossRefGoogle Scholar
[3]Chang, C. C. and Keisler, H. J., Model theory, North-Holland, Amsterdam, 1973.Google Scholar
[4]Compton, K. J., Laws in logic and combinatorics, Algorithms and order (Rival, I., editor), Kluwer Academic Publishers, Dordrecht, 1989, pp. 353–383.CrossRefGoogle Scholar
[5]Fouché, W. L., Identifying randomness given by high descriptive complexity, Acta Applicandae Mathematicae, vol. 34 (1994), pp. 313–328.CrossRefGoogle Scholar
[6]Fouché, W. L., Descriptive complexity and reflective properties of combinatorial configurations, Journal of the London Mathematical Society, Second Series, vol. 54 (1996), pp. 199–208.CrossRefGoogle Scholar
[7]Fraïssé, R., Sur l'extension aux relations de quelques propriétés des ordres, Annates Scientifiques de l'École Normale Superieure, Quatrième Série, vol. 71 (1954), pp. 363–388.CrossRefGoogle Scholar
[8]Gács, P., Randomness and probability—complexity of description, Encyclopedia of statistical sciences, John Wiley & Sons, 1986, pp. 551–555.Google Scholar
[9]Gács, P., A review of G. Chaitin's algorithmic information theory, this Journal, vol. 54 (1989), pp. 624–627.Google Scholar
[10]Hinman, P. G., Recursion-theoretic hierarchies, Springer-Verlag, New York, 1978.CrossRefGoogle Scholar
[11]Hodges, W., Model theory, Cambridge University Press, Cambridge, 1993.CrossRefGoogle Scholar
[12]Jockusch, C. G. Jr., Ramsey's theorem and recursion theory, this Journal, vol. 37 (1972), pp. 268–280.Google Scholar
[13]Kleitman, D. J. and Rothschild, B. L., Asymptotic enumeration of partial orders on a finite set, Transactions of the American Mathematical Society, vol. 205 (1975), pp. 205–220.CrossRefGoogle Scholar
[14]Kolmogorov, A. N., Three approaches to the quantitative definition of information, Probl. Inform. Transmission, vol. 1 (1965), pp. 1–7.Google Scholar
[15]Kolmogorov, A. N. and Uspenskii, V. A., Algorithms and randomness, Theory Probability and its Applications, vol. 32 (1987), pp. 389–412.CrossRefGoogle Scholar
[16]Martin-Löf, P., The definition of random sequences, Information and Control, vol. 9 (1966), pp. 602–619.CrossRefGoogle Scholar
[17]Rado, R., Universal graphs and universal functions, Acta Arithmetica, vol. 9 (1964), pp. 393–407.CrossRefGoogle Scholar
[18]Ramsey, F. P., On a problem of formal logic, Proceedings of the London Mathematical Society, vol. 30 (1930), pp. 264–286.CrossRefGoogle Scholar
[19]Specker, E., Ramsey's theorem does not hold in recursive set theory, Studies in logic and the foundations of mathematics, North-Holland, Amsterdam, 1971.Google Scholar
[20]Vitányi, P. and Li, M., An introduction to Kolmogorov complexity and its applications, Springer-Verlag, 1993.Google Scholar