Real Analysis Exchange
- Real Anal. Exchange
- Volume 39, Number 2 (2014), 323-334.
The Class of Purely Unrectifiable Sets in \(\ell_2\) is \(\Pi_1^1\)-complete
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.
Real Anal. Exchange, Volume 39, Number 2 (2014), 323-334.
First available in Project Euclid: 30 June 2015
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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