We construct two recursive models of fragments of set theory. We also show that the fragments of Kripke-Platek set theory that prove $ \varepsilon$-induction for $ \Sigma_1$-formulas have no recursive models but the standard model of the hereditarily finite sets.
"A Note on Recursive Models of Set Theories." Notre Dame J. Formal Logic 42 (2) 109 - 115, 2001. https://doi.org/10.1305/ndjfl/1054837937