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Natural examples of $\boldsymbol{\Pi}_{5}^{0}$ -complete sets in analysis

Author(s): Nikolaos Efstathiou Sofronidis
Journal: Proc. Amer. Math. Soc. 130 (2002), 1177-1182.
MSC (2000): Primary 03E15; Secondary 30D20
Posted: September 28, 2001
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Abstract: The purpose of this paper is to show that given any non-negative real number $\alpha$ , the set of entire functions whose order is equal to $\alpha$ is $\boldsymbol{\Pi}_{3}^{0}$ -complete, and the set of all sequences of entire functions whose orders converge to $\alpha$ is $\boldsymbol{\Pi}_{5}^{0}$ -complete.

References:

[1]: E. HILLE, Analytic Function Theory, Volume 1, Ginn and Company, New York, 1959. MR 21:6415
[2]: E. HILLE, Analytic Function Theory, Volume 2, Ginn and Company, Boston, 1962. MR 34:1490
[3]: A. S. KECHRIS, Classical Descriptive Set Theory, Springer-Verlag, New York, 1995. MR 96e:03057
[4]: H. J. ROGERS, Theory of Recursive Functions and Effective Computability, McGraw Hill, New York, 1967. MR 37:61
[5]: N. E. SOFRONIDIS, Topics in Descriptive Set Theory related to Equivalence Relations, Complex Borel and Analytic Sets, Ph.D. Thesis, California Institute of Technology, 1999

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Additional Information:

Nikolaos Efstathiou Sofronidis
Affiliation: 19 Stratigou Makryianni Street, Thessaloniki 54635, Greece
Email: sofnik@otenet.gr

DOI: 10.1090/S0002-9939-01-06180-9
PII: S 0002-9939(01)06180-9
Received by editor(s): July 20, 2000
Received by editor(s) in revised form: September 29, 2000
Posted: September 28, 2001
Additional Notes: The contents of this paper comprise part of the author's doctoral dissertation written under the direction of Professor A. S. Kechris at the California Institute of Technology.
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 2001, American Mathematical Society


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