# Adding a lot of random reals by adding a few

## TL;DR

This paper investigates how adding a small number of random reals to a model can result in a larger number of random reals being added to an extension, revealing complex interactions in set-theoretic models.

## Contribution

It introduces a framework for understanding how adding a few random reals can lead to the addition of many more in extended models of ZFC.

## Key findings

- Adding $ ext{κ}$-many random reals over $V_1$ can add $ ext{λ}$-many over $V$ with $ ext{λ} > ext{κ}$
- The study characterizes conditions under which small additions produce large extensions
- Provides new insights into the behavior of random reals in models of set theory

## Abstract

We study pairs $(V, V_1)$ of models of $ZFC$ such that adding $\kappa$-many random reals over $V_1$ adds $\lambda$-many random reals over $V$, for some $\lambda > \kappa.$