Erik Walsberg

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math.LO2019

Fractals and the monadic second order theory of one successor

Philipp Hieronymi, Erik Walsberg

We show that if $X$ is virtually any classical fractal subset of $R^{n}$ , then $(R, <, +, X)$ interprets the monadic second-order theory of $(N, + 1)$ . This res…

math.LO2015

The Hausdorff dimension of metric spaces definable in o-minimal expansions of the real field

Jana Maříková, Erik Walsberg

Let $R$ be an o-minimal expansion of the real field. We show that the Hausdorff dimension of an $R$ -definable metric space is an $R$ -definable function of the parameters defining t…