Combining Resurrection and Maximality

TL;DR

This paper demonstrates that the resurrection axiom and the maximality principle can be consistently combined across different forcing classes, exploring their overlap through the local maximality principle.

Contribution

It introduces a method to combine resurrection and maximality principles and analyzes their relationship using the local maximality principle.

Findings

Resurrection and maximality can be jointly satisfied in various forcing contexts.

The extent of overlap between resurrection and maximality is characterized.

The local maximality principle provides insights into their interaction.

Abstract

It is shown that the resurrection axiom and the maximality principle may be consistently combined for various iterable forcing classes. The extent to which resurrection and maximality overlap is explored via the local maximality principle.