We prove monadic second order limit laws for ordinals stemming from segments of some prominent proof-theoretic ordinals like \(\omega^\omega,\varepsilon_0,\Gamma_0,\ldots\). The results are based on a combination of automata theoretic results, tree enumeration theory and Tauberian methods. We believe that our results will hold in very general contexts.

Some results have been obtained jointly with Alan R. Woods (who unfortunately passed away in 2011).