Local Definability of HOD in L(ℝ)

2023/08/02 by Obrad Kasum, Kasum, Obrad
Computer Science · Mathematics · #03E45 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2308.01072

openalex publication_date 2023/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We show that in L(ℝ), assuming large cardinals, HOD ∥η^+HOD is locally definable from HOD ∥η for all HOD-cardinals η∈ [\boldsymbolδ²₁,Θ). This is a further elaboration of the statement "HOD^L(ℝ) is a core model below Θ" made by John Steel.

Related

• The HOD Hypothesis and a supercompact cardinal
• On the optimality of the HOD dichotomy
• HOD in inner models with Woodin cardinals
• Analysis of HOD for Admissible Structures
• Local mantles of L[x]