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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Nikolaos Efstathiou Sofronidis
Journal: Proc. Amer. Math. Soc. 130 (2002), 1177-1182
MSC (2000): Primary 03E15; Secondary 30D20
Published electronically: September 28, 2001
MathSciNet review: 1873794
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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.


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Additional Information

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

DOI: http://dx.doi.org/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
Published electronically: 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.
Article copyright: © Copyright 2001 American Mathematical Society