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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Natural examples of $\boldsymbol {\Pi }_{5}^{0}$-complete sets in analysis
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by Nikolaos Efstathiou Sofronidis
Proc. Amer. Math. Soc. 130 (2002), 1177-1182
DOI: https://doi.org/10.1090/S0002-9939-01-06180-9
Published electronically: 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
  • Einar Hille, Analytic function theory. Vol. 1, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass., 1959. MR 0107692
  • Einar Hille, Analytic function theory. Vol. II, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass.-New York-Toronto, 1962. MR 0201608
  • Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597, DOI 10.1007/978-1-4612-4190-4
  • Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto-London, 1967. MR 0224462
  • 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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Bibliographic Information
  • Nikolaos Efstathiou Sofronidis
  • Affiliation: 19 Stratigou Makryianni Street, Thessaloniki 54635, Greece
  • Email: sofnik@otenet.gr
  • 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.
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 1177-1182
  • MSC (2000): Primary 03E15; Secondary 30D20
  • DOI: https://doi.org/10.1090/S0002-9939-01-06180-9
  • MathSciNet review: 1873794