# Generic large cardinals as axioms

## TL;DR

The paper critiques the idea of resolving the continuum hypothesis and similar questions by adopting generic large cardinal axioms, arguing against this approach.

## Contribution

It provides a critical analysis of using generic large cardinal axioms as a method to settle classical independent problems.

## Key findings

- Argues against the effectiveness of generic large cardinal axioms for solving continuum hypothesis
- Highlights limitations of axiomatic approaches based on large cardinals
- Questions the philosophical and mathematical validity of this method

## Abstract

We argue against Foreman's proposal to settle the continuum hypothesis and other classical independent questions via the adoption of generic large cardinal axioms.