Hjorth’s Reflection Argument
Abstract
Abstract In [7], Hjorth, assuming $\mathsf {{AD+ZF+DC}}$ , showed that there is no sequence of length $\omega _2$ consisting of distinct $\boldsymbol {\Sigma }^1_2$ -sets. We show that the same theory implies that for $n\geq 0$ , there is no sequence of length $\boldsymbol {\delta }^1_{2n+2}$ consisting of distinct $\boldsymbol {\Sigma }^1_{2n+2}$ sets. The theorem settles Question 30.21 of [16], which was also conjectured by Kechris in [17] (see Conjecture in Chapter 4 of [17] and the last paragraph of Chapter 4 of [17]).
Fields of Study & Subjects
Advanced Topology and Set Theory
Limits and Structures in Graph Theory
Geometric and Algebraic Topology
Publication details
- Journal / source
- Forum of Mathematics Sigma
- Volume
- 14
- Publication date
- 1 January 2026
- Language
- EN