We employ an infinite-signature Hrushovski amalgamation construction to yield two results in Recursive Model Theory. The first result, that there exists a strongly minimal theory whose only recursively presentable models are the prime and saturated models, adds a new spectrum to the list of known possible spectra. The second result, that there exists a strongly minimal theory in a finite language whose only recursively presentable model is saturated, gives the second non-trivial example of a spectrum produced in a finite language.
"A new spectrum of recursive models using an amalgamation construction." J. Symbolic Logic 76 (3) 883 - 896, September 2011. https://doi.org/10.2178/jsl/1309952525