The strong reflecting property and Harrington's Principle

TL;DR

This paper explores the strong reflecting property for L-cardinals, characterizes Harrington's Principle and its generalization, and examines their interrelations within set theory.

Contribution

It provides a comprehensive characterization of the strong reflecting property for L-cardinals and clarifies the relationship between this property and Harrington's Principle.

Findings

Characterization of the strong reflecting property for all ω_n in L

Formalization of Harrington's Principle HP(L) and its generalization

Analysis of the relationship between the strong reflecting property and HP(L)

Abstract

In this paper we characterize the strong reflecting property for $L$-cardinals for all $\omega_n$, characterize Harrington's Principle $HP(L)$ and its generalization and discuss the relationship between the strong reflecting property for $L$-cardinals and Harrington's Principle $HP(L)$.