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References
Calvert W., Cenzer D., Harizanov V., Morozov A.: Effective categoricity of equivalence structures. Ann. Pure Appl. Logic 141, 61–78 (2006)
Calvert, W., Goncharov, S.S., Knight, J.F.: Computable structures of Scott rank \({\omega_1^{CK}}\) in familiar classes. In: Gao, S., Jackson, S., Zhang, Y. (eds.) Advances in Logic. Con. Math., vol. 45, pp. 49–66 (2007)
Calvert W., Knight J.F., Millar J.: Computable trees of Scott rank \({\omega_1^{CK}}\), and computable approximability. J. Symb. Logic 71, 283–298 (2006)
Cenzer D., Remmel, J.B.: Complexity-theoretic model theory and algebra. In: Ershov, Y., Goncharov, S.S., Nerode, A., Remmel, J.B. (eds.) Handbook of Recursive Mathematics, vol. I. Studies in Logic and Found. Math., vol. 138, pp. 381–513 (1998)
Cholak P., Goncharov S., Khoussainov B., Shore R.A.: Computably categorical structures and expansions by constants. J. Symb. Logic 64, 13–37 (1999)
Denef J., Lipshitz L.: Diophantine sets over some rings of algebraic integers. J. London Math. Soc. 18, 385–391 (1978)
Dolich A., Laskowski M.C., Raichev A.: Model completeness for trivial, uncountably categorical theories of Morley Rank 1. Arch. Math. Logic 45, 931–945 (2006)
Downey R.G.: Every recursive Boolean algebra is isomorphic to one with incomplete atoms. Ann. Pure Appl. Logic 60, 193–206 (1993)
Downey R.G., Moses M.F.: Recursive linear orders with incomplete successivities. Trans. Am. Math. Soc. 326, 653–668 (1991)
Downey R.G., Goncharov S.S., Hirschfeldt D.: Degree spectra of relations on Boolean algebras. Algebra and Logic 42, 105–111 (2003)
Dzgoev V.D., Gončarov S.S.: Autostability of models. Algebra i Logika 19, 45–58 (1980)
Davis, M., Matiyasevich, Yu., Robinson, J.: Hilbert’s tenth problem. Diophantine equations: Positive aspects of a negative solution. In: Proc. Sympos. Pure Math., vol. 28. Amer. Math. Soc., Providence, RI, pp. 323–378 (1976)
Gončarov S.S.: The problem of the number of nonautoequivalent constructivizations. Algebra i Logika 19, 621–639 (1980)
Goncharov S.S., Harizanov V.S., Laskowski M.C., Lempp S., McCoy C.F.D.: Trivial, strongly minimal theories are model complete after naming constants. Proc. Am. Math. Soc. 131, 3901–3912 (2003)
Herrmann E.: Infinite chains and antichains in computable partial orderings. J. Symb. 66, 923–934 (2001)
Shapiro H.N., Shlapentokh A.: Diophantine relations between algebraic number fields. Comm. Pure Appl. Math. 42, 1113–1122 (1989)
Jockusch C.G. Jr: Ramsey’s theorem and recursion theory. J. Symb. Logic 37, 268–280 (1972)
Khoussainov B.M.: The algorithmic dimension of unars. Algebra i Logika 27, 479–494 (1988)
Khoussainov B.M., Laskowski M.C., Lempp S., Solomon R.: On the computability-theoretic complexity of trivial, strongly minimal models. Proc. Am. Math. Soc. 135, 3711–3721 (2007)
Marker D.: Non \({\Sigma_{n}}\) axiomatizable almost strongly trivial theories. J. Symb. Logic 54, 921–927 (1989)
Marker D.: Model Theory. An Introduction. Graduate Texts in Mathematics, vol. 217. Springer, Berlin (2002)
Millar, J., Sacks, G.E.: Atomic models higher up. Ann. Pure Appl. Logic (to appear)
Pillay A., Poizat B.: Corps at chirurgie. J. Symb. Logic 60, 528–533 (1995)
Remmel J.B.: Recursive isomorphism types of recursive Boolean algebras. J. Symb. Logic 46, 572–594 (1981)
Remmel J.B.: Recursively categorical linear orderings. Proc. Am. Math. Soc. 83, 387–391 (1981)
Shlapentokh A.: Hilbert’s Tenth Problem: Diophantine Classes and Extensions to Global Fields. Cambridge University Press, London (2006)
Shlapentokh A.: Diophantine definability and decidability in the extensions of degree 2 of totally real fields. J. Algebra 313, 846–896 (2007)
Ventsov Y.G.: Algorithmic properties of branching models. Algebra i Logika 25, 369–383 (1986)
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Cenzer, D., Harizanov, V., Marker, D. et al. Preface. Arch. Math. Logic 48, 1–6 (2009). https://doi.org/10.1007/s00153-008-0111-5
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DOI: https://doi.org/10.1007/s00153-008-0111-5