Monadic second order limit laws for natural well orderings
Andreas Weiermann · arXiv (Cornell University) · 2020
By combining classical results of Büchi, some elementary Tauberian theorems and some basic tools from logic and combinatorics we show that every ordinal $α$ with $\varepsilon_0\geq α\geq ω^ω$ satisfies a natural monadic second order limit law and that every ordinal $α$ with $ω^ω>α\geq ω$ satisfies a natural monadic second order Cesaro limit law. In both cases we identify as usual $α$ with the class of substructures $\{β:β