The Diagonal Strong Reflection Principle and its fragments

TL;DR

This paper introduces a diagonal strong reflection principle, explores its fragments related to forcing classes, analyzes their relationships with forcing axioms, and presents consequences including diagonal stationary reflection principles.

Contribution

It presents a new diagonal version of the strong reflection principle, analyzes its fragments, and distinguishes these from related axioms, advancing understanding of reflection principles in set theory.

Findings

Introduces a diagonal strong reflection principle.

Analyzes relationships with forcing axioms.

Separates diagonal strong reflection principles from related axioms.

Abstract

A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the corresponding forcing axioms and the corresponding fragments of the strong reflection principle are analyzed, and consequences are presented. Some of these consequences are ``exact'' versions of diagonal stationary reflection principles of sets of ordinals. We also separate some of these diagonal strong reflection principles from related axioms.