Real Analysis Exchange

The Class of Purely Unrectifiable Sets in \(\ell_2\) is \(\Pi_1^1\)-complete

Vadim Kulikov

Full-text: Open access

Abstract

The space \(F(\ell_2)\) of all closed subsets of \(\ell_2\) is a Polish space. We show that the subset \(P\subset F(\ell_2)\) consisting of the purely \(1\)-unrectifiable sets is \(\Pi_1^1\)-complete.

Article information

Source
Real Anal. Exchange, Volume 39, Number 2 (2014), 323-334.

Dates
First available in Project Euclid: 30 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.rae/1435669998

Mathematical Reviews number (MathSciNet)
MR3365377

Zentralblatt MATH identifier
1354.03064

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
Secondary: 28E15: Other connections with logic and set theory

Keywords
purely unrectifiable co-analytic complete Hilbert space

Citation

Kulikov, Vadim. The Class of Purely Unrectifiable Sets in \(\ell_2\) is \(\Pi_1^1\)-complete. Real Anal. Exchange 39 (2014), no. 2, 323--334. https://projecteuclid.org/euclid.rae/1435669998


Export citation