@inproceedings{952c3a58cf77448596ed46cd5ba5d644,

title = "Degrees of categoricity for prime and homogeneous models",

abstract = "We study effective categoricity for homogeneous and prime models of a complete theory. For a computable structure S, the degree of categoricity of S is the least Turing degree which can compute isomorphisms among arbitrary computable copies of 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 0(ω+1) is the degree of categoricity for a homogeneous model. We prove that any Turing degree which is d.c.e. in and above 0(n), where 3 ≤ n < ω, is the degree of categoricity for a prime Heyting algebra.",

keywords = "Autostability spectrum, Categoricity spectrum, Computable categoricity, Computable structure, Degree of categoricity, Heyting algebra, Homogeneous model, Prime model, COMPUTABLE CATEGORICITY, SPECTRA, AUTOSTABILITY",

author = "Nikolay Bazhenov and Margarita Marchuk",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/978-3-319-94418-0_4",

language = "English",

isbn = "9783319944173",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag GmbH and Co. KG",

pages = "40--49",

editor = "F Manea and RG Miller and D Nowotka",

booktitle = "Sailing Routes in the World of Computation - 14th Conference on Computability in Europe, CiE 2018, Proceedings",

address = "Germany",

note = "14th Conference on Computability in Europe, CiE 2018 ; Conference date: 30-07-2018 Through 03-08-2018",

}