Convergence for irrational root-growth exponents

Determine whether the averaging logic with global mean, local mean, supremum, and Lipschitz connectives satisfies a convergence law on Erdős–Rényi random featured graphs with edge probability n^{-\alpha} for irrational \alpha.

Background

The discussion distinguishes irrational root-growth exponents from rational ones. For first-order logic, irrational exponents are associated with a zero-one law, but extending convergence to the paper’s richer aggregate term language would require adapting the intricate argument of Shelah and Spencer. The authors explicitly identify the irrational case as unresolved.