TL;DR
This paper establishes general theorems for maintaining the Dependent Choice axiom in symmetric extensions, providing new and folklore results that facilitate simpler consistency proofs in set theory.
Contribution
It introduces new theorems for preserving Dependent Choice in symmetric extensions and applies them to simplify consistency proofs.
Findings
General theorems for preserving Dependent Choice
Application to various constructions for consistency proofs
Unwritten folklore results formalized
Abstract
We prove some general theorems for preserving Dependent Choice when taking symmetric extensions, some of which are unwritten folklore results. We apply these to various constructions to obtain various simple consistency proofs.
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