Abstract
We study effective categoricity for homogeneous and prime models of a complete theory. For a computable structure \(\mathcal {S}\), the degree of categoricity of \(\mathcal {S}\) is the least Turing degree which can compute isomorphisms among arbitrary computable copies of \(\mathcal {S}\). We build new examples of degrees of categoricity for homogeneous models and for prime Heyting algebras, i.e. prime models of a complete extension of the theory of Heyting algebras. We show that \(\mathbf {0}^{(\omega +1)}\) is the degree of categoricity for a homogeneous model. We prove that any Turing degree which is d.c.e. in and above \(\mathbf {0}^{(n)}\), where \(3 \le n <\omega \), is the degree of categoricity for a prime Heyting algebra.
N. Bazhenov was supported by RFBR project No. 16-31-60058 mol_a_dk. M. Marchuk was supported by RFBR project No. 17-01-00247.
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Bazhenov, N., Marchuk, M. (2018). Degrees of Categoricity for Prime and Homogeneous Models. In: Manea, F., Miller, R., Nowotka, D. (eds) Sailing Routes in the World of Computation. CiE 2018. Lecture Notes in Computer Science(), vol 10936. Springer, Cham. https://doi.org/10.1007/978-3-319-94418-0_4
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