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].
Publié le : 1999-12-14
Classification:
Descriptive Set Theory,
Complete Analytic Set,
Linear Order,
Iterates of Continuous Functions,
04A15,
26A21
@article{1183745934,
author = {Beleznay, Ferenc},
title = {The Complexity of the Collection of Countable Linear Orders of the Form I + I},
journal = {J. Symbolic Logic},
volume = {64},
number = {1},
year = {1999},
pages = { 1519-1526},
language = {en},
url = {http://dml.mathdoc.fr/item/1183745934}
}
Beleznay, Ferenc. The Complexity of the Collection of Countable Linear Orders of the Form I + I. J. Symbolic Logic, Tome 64 (1999) no. 1, pp. 1519-1526. http://gdmltest.u-ga.fr/item/1183745934/