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\(\Delta_{2}^{0}\)-categoricity in Boolean algebras and linear orderings. (English) Zbl 1016.03036
Summary: We characterize \(\varDelta _2^0\)-categoricity in Boolean algebras and linear orderings under some extra effectiveness conditions. We begin with a study of the relativized notion in these structures.

MSC:
03C57 Computable structure theory, computable model theory
03D45 Theory of numerations, effectively presented structures
03C35 Categoricity and completeness of theories
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[1] Ash, C.J.; Knight, J.F., Computable structures and the hyperarithmetical hierarchy, (2000), North-Holland Publishing Company Amsterdam · Zbl 0960.03001
[2] Ash, C.J.; Knight, J.F.; Manasse, M.; Slaman, T., Generic copies of countable structures, Ann. pure appl. logic, 42, 195-205, (1989) · Zbl 0678.03012
[3] Chang, C.C.; Keisler, H.J., Model theory, (1973), North-Holland Amsterdam · Zbl 0276.02032
[4] Chisholm, J., Effective model theory vs. recursive model theory, J. symbolic logic, 55, 1168-1191, (1990) · Zbl 0722.03030
[5] Downey, R., Computability theory and linear ordering, (), 823-976 · Zbl 0941.03045
[6] S.S. Goncharov, Autostability and computable families of constructivizations. Algebra Logic 14 (1975) 647-680 (Russian), 392-409 (English).
[7] S.S. Goncharov, The quantity of non-autoequivalent constructivizations, Algebra Logic 16 (1977) 257-282 (Russian), 169-185 (English).
[8] S.S. Goncharov, Autostability of models and abelian groups, Algebra Logic 19 (1980) 23-44 (Russian), 13-27 (English). · Zbl 0468.03022
[9] S.S. Goncharov, The problem of the number of non-self-equivalent constructivizations, Algebra Logic 19 (1980) 621-639 (Russian), 401-414 (English).
[10] S.S. Goncharov, V.D. Dzgoev, Autostability of models, Algebra Logic 19 (1980) 45-58 (Russian), 28-36 (English). · Zbl 0468.03023
[11] Hungerford, T., Algebra, (1974), Springer Berlin
[12] J.F. Knight, M. Stob, Computable Boolean Algebras, preprint. · Zbl 0974.03041
[13] Koppelberg, S., Handbook of Boolean algebras, (1989), North-Holland Amsterdam
[14] O.V. Kudinov, A criterion for the autostability of 1-decidable models, Algebra Logic 31 (1992) 479-492 (Russian), 284-292 (English).
[15] Moses, M., Recursive linear orderings with recursive successivities, Ann. pure appl. logic, 27, 253-264, (1984) · Zbl 0572.03025
[16] Remmel, J.B., Recursive isomorphism types of recursive Boolean algebras, J. symbolic logic, 46, 596-616, (1981) · Zbl 0543.03031
[17] Remmel, J.B., Recursively categorical linear orderings, Proc. AMS, 83, 387-391, (1981) · Zbl 0493.03022
[18] La Roche, P., Recursively presented Boolean algebras, Notices AMS, 24, A552-A553, (1977)
[19] Soare, R.I., Recursively enumerable sets and degrees, (1987), Springer Berlin
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