Erdős–Rado theorem

In partition calculus, part of combinatorial set theory, a branch of mathematics, the Erdős–Rado theorem is a basic result extending Ramsey's theorem to uncountable sets.

It is named after Paul Erdős and Richard Rado.

[1] It is sometimes also attributed to Đuro Kurepa who proved it under the additional assumption of the generalised continuum hypothesis,[2] and hence the result is sometimes also referred to as the Erdős–Rado–Kurepa theorem.

This is sharp in the sense that expr(κ)+ cannot be replaced by expr(κ) on the left hand side.

The above partition symbol describes the following statement.