# Infinite forcing and the generic multiverse

## TL;DR

This paper introduces a model-theoretic technique using Robinson infinite forcing applied to Cohen forcing models of ZFC, aiming to unify perspectives on generic absoluteness principles.

## Contribution

It presents a novel application of infinite forcing to Cohen models, offering a new unified approach to understanding generic absoluteness.

## Key findings

- Infinite forcing models are complete in a model-theoretic sense.
- Unified perspective on generic absoluteness principles is proposed.
- Technique bridges Cohen forcing and model completeness.

## Abstract

In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing. This technique will be used to suggest a unified perspective on generic absoluteness principles.