An $\omega$-word $s \in \Sigma^\omega$ is eventually periodic if it is of the form $s = uv^\omega$ for finite words $u, v \in \Sigma^*$.
I want to show that the set of all eventually periodic words is not buchi-recognizable.
I do not know how to proceed. My attempt was to find a part of the word and then pump it indefinitely to get something that is not in the language. However, pumping right away does not seem to work since that would give an eventually periodic string again.