# Some mutually inconsistent generic large cardinals

## TL;DR

This paper explores classes of generic large cardinal axioms that are individually consistent but cannot all be true simultaneously, extending Woodin's previous work in the area.

## Contribution

It identifies specific classes of generic large cardinal axioms that are consistent on their own but mutually incompatible.

## Key findings

- Certain classes of generic large cardinal axioms are mutually inconsistent.
- The results extend Woodin's earlier findings on large cardinals.
- The work clarifies the landscape of large cardinal axioms and their consistency relations.

## Abstract

Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.