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Uniformity in computable structure theory. (Russian, English) Zbl 1063.03018
Algebra Logika 42, No. 5, 566-593 (2003); translation in Algebra Logic 42, No. 5, 318-332 (2003).
Summary: We investigate the effects of adding uniformity requirements to concepts in computable structure theory such as computable categoricity (of a structure) and intrinsic computability (of a relation on a computable structure). We consider and compare two different notions of uniformity, previously studied by O. V. Kudinov and by Yu. G. Ventsov. We discuss some of their results and establish new ones, while also exploring the connections with the relative computable structure theory of C. Ash, J. Knight, M. Manasse, and T. Slaman [Ann. Pure Appl. Logic 42, No. 3, 195–205 (1989; Zbl 0678.03012)] and J. Chisholm [J. Symb. Log. 55, No. 3, 1168–1191 (1990; Zbl 0722.03030)] and with previous work of C. J. Ash, J. F. Knight and T. A. Slaman [Fundam. Math. 142, No. 2, 147–161 (1993; Zbl 0809.03024)] on uniformity in a general computable structure-theoretical setting.

03C57 Computable structure theory, computable model theory
03D45 Theory of numerations, effectively presented structures