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ω-powers and descriptive set theory

Published online by Cambridge University Press:  12 March 2014

Dominique Lecomte
Dominique Lecomte*
Affiliation:
Université Paris 6, Equipe D'Analyse Fonctionnelle, Tour 46-0. Boîte 186, 4. Place Jussieu 75 252 Paris Cedex 05., FranceUniversité de Picardie, I.U.T. de L'Oise Site de Creil, 13. Allée de La Faïencerie 60 107 Creil., France, E-mail: lecomte@moka.ccr.jussieu.fr
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Abstract

We study the sets of the infinite sentences constructible with a dictionary over a finite alphabet, from the viewpoint of descriptive set theory. Among others, this gives some true co-analytic sets. The case where the dictionary is finite is studied and gives a natural example of a set at level ω of the Wadge hierarchy.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 4 , December 2005, pp. 1210 - 1232
Copyright
Copyright © Association for Symbolic Logic 2005

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References

REFERENCES

[1]Finkel, O., Topological properties of omega context free languages, Theoretical Computer Science, vol. 262 (2001), pp. 669–697.CrossRefGoogle Scholar
[2]Finkel, O., Borel hierarchy and omega context free languages, Theoretical Computer Science, vol. 290 (2003), no. 3, pp. 1385–1405.CrossRefGoogle Scholar
[3]Kechris, A. S., Classical descriptive set theory, Springer-Verlag, 1995.CrossRefGoogle Scholar
[4]Kechris, A. S., On the concept of Π11 -completeness, Proceedings of the American Mathematical Society, vol. 125 (1997), no. 6, pp. 1811–1814.CrossRefGoogle Scholar
[5]Levy, A., Basic set theory, Springer-Verlag, 1979.CrossRefGoogle Scholar
[6]Lothaire, M., Algebraic combinatorics on words, Cambridge University Press, 2002.CrossRefGoogle Scholar
[7]Louveau, A., A separation theorem for Σ11 sets, Transactions of the American Mathematical Society, vol. 260 (1980), pp. 363–378.Google Scholar
[8]Moschovakis, Y. N., Descriptive set theory, North-Holland, 1980.Google Scholar
[9]Simonnet, P., Automates et théorie descriptive, Ph.D. thesis, Université Paris 7, 03 1992.Google Scholar
[10]Staiger, L., ω-languages, Handbook of formal languages (Rozenberg, G. and Salomaa, A., editors), vol. 3. Springer-Verlag, 1997.Google Scholar
[11]Staiger, L., On ω-power languages, New trends in formal languages, control, cooperation and combinatorics, Lecture Notes in Computer Science, vol. 1218, Springer-Verlag, 1997. pp. 377–393.Google Scholar