Northcott property and universality of higher degree forms

Let $K$ be a totally real number field, $d$ a positive integer, and $Q$ a higher degree form over $K$. We prove that there are at most finitely many totally real extensions $L/K$ of degree $d$ such that $Q$ over $L$ is universal. Further, we show that there are no universal forms over totally real infinite extensions of $\mathbb{Q}$ having the Northcott property.
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