# Adding many random reals may add many Cohen reals

## TL;DR

The paper investigates how forcing with two copies of random reals over an infinite cardinal can lead to the addition of many Cohen reals, revealing interactions between different forcing notions.

## Contribution

It demonstrates that forcing with two products of random reals can add a generic filter for Cohen reals, showing a new interaction between these forcing notions.

## Key findings

- Forcing with R(κ)×R(κ) adds a generic filter for C(κ).
- Adding many random reals can result in adding many Cohen reals.
- The result holds for any infinite cardinal κ.

## Abstract

Let $\kappa$ be an infinite cardinal. Then, forcing with $\mathbb{R}(\kappa)$$\times$$\mathbb{R}(\kappa)$ adds a generic filter for $\mathbb{C}(\kappa);$ where $\mathbb{R}(\kappa)$ and $\mathbb{C}(\kappa)$ are the forcing notions for adding $\kappa$-many random reals and adding $\kappa$-many Cohen reals respectively.