Journal of Symbolic Logic

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

Ferenc Beleznay

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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 $\circ$ 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 [K1] and on p. 4 of [B].

Article information

Source
J. Symbolic Logic, Volume 64, Issue 4 (1999), 1519-1526.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745934

Mathematical Reviews number (MathSciNet)
MR1780067

Zentralblatt MATH identifier
0944.03046

JSTOR
links.jstor.org

Subjects
Primary: 04A15
Secondary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]

Keywords
Descriptive Set Theory Complete Analytic Set Linear Order Iterates of Continuous Functions

Citation

Beleznay, Ferenc. The Complexity of the Collection of Countable Linear Orders of the Form I + I. J. Symbolic Logic 64 (1999), no. 4, 1519--1526. https://projecteuclid.org/euclid.jsl/1183745934


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