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The Complexity of the Collection of Countable Linear Orders of the form I + I

Published online by Cambridge University Press:  12 March 2014

Ferenc Beleznay
Ferenc Beleznay*
Affiliation:
Department of Analysis, Eötvös Loránd University, Budapest, Rákóczi ÚT 5. 1088., Hungary, E-mail: beleznay@cs.elte.hu
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Abstract

First we prove that the set of countable linear orders of the form I + I form a complete analytic set. As a consequence of this we improve a result of Humke and Laczkovich, who showed in [HL] that the set of functions of the form f º f form a true analytic set in C[0,1]. We show that these functions form a complete analytic set, solving a problem mentioned on p. 215 of [Kl] and on p. 4 of [B]

Keywords

Descriptive set theory, complete analytic set, linear order, iterates of continuous functions
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999 , pp. 1519 - 1526
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

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