UNREACHABILITY OF INDUCTIVE-LIKE POINTCLASSES IN $L(\mathbb {R})$
Abstract
Abstract In [3], Hjorth proved from $ZF + AD + DC$ that there is no sequence of distinct $\boldsymbol {\Sigma ^1_2}$ sets of length $\boldsymbol {\delta ^1_2}$ . Sargsyan [11] extends Hjorth’s technique to show there is no sequence of distinct $\boldsymbol {\Sigma ^1_{2n}}$ sets of length $\boldsymbol {\delta ^1_{2n}}$ . Sargsyan conjectured an analogous property is true for any regular Suslin pointclass in $L(\mathbb {R})$ —i.e., if $\kappa $ is a regular Suslin cardinal in $L(\mathbb {R})$ , then there is no sequence of distinct $\kappa $ -Suslin sets of length $\kappa ^+$ in $L(\mathbb {R})$ . We prove this in the case that the pointclass $S(\kappa )$ is inductive-like.
Fields of Study & Subjects
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
semigroups and automata theory
Publication details
- Journal / source
- Journal of Symbolic Logic
- Publisher
- Cambridge University Press (CUP)
- Volume
- 91
- Issue
- 1
- Pages
- 175–209
- Publication date
- 12 January 2026
- Language
- EN