A New Spectrum of Recursive Models
André Nies · Notre Dame Journal of Formal Logic · 1999
We describe a strongly minimal theory S in an effective language such that, in the chain of countable models of S, only the second model has a computable presentation. Thus there is a spectrum of an $ \omega_{1}^{}$-categorical theory which is neither upward nor downward closed. We also give an upper bound on the complexity of spectra.