Geodesic
Strongly minimal theories with recursive models
Journal of the European Mathematical Society, Tome 20 (2018) no. 7, pp. 1561-1594 Cet article a éte moissonné depuis la source EMS Press

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We give effectiveness conditions on a strongly minimal theory T guaranteeing that all countable models have computable copies. In particular, we show that if T is strongly minimal and for all n≥1, T∩∃n+2​ is Δn0​, uniformly in n, then every countable model has a computable copy. A longstanding question of computable model theory asked whether for a strongly minimal theory with one computable model, every countable model has an arithmetical copy. Relativizing our main result, we get the fact that if there is one computable model, then every countable model has a Δ40​ copy.
DOI : 10.4171/jems/793
Classification : 03-XX
Keywords: Strongly minimal, worker argument, recursive models, computable models 
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     author = {Uri Andrews and Julia F. Knight},
     title = {Strongly minimal theories with recursive models},
     journal = {Journal of the European Mathematical Society},
     pages = {1561--1594},
     year = {2018},
     volume = {20},
     number = {7},
     doi = {10.4171/jems/793},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/793/}
}
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Uri Andrews; Julia F. Knight. Strongly minimal theories with recursive models. Journal of the European Mathematical Society, Tome 20 (2018) no. 7, pp. 1561-1594. doi: 10.4171/jems/793

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