Uniformity in Computable Structure Theory
Status: published in Algebra
and Logic, 42 (2003) 318 - 332.
version and preprint
Abstract. 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 Kudinov and by
Ventsov. We discuss some of their results and establish new ones,
while also exploring the connections with the relative computable
structure theory of Ash, Knight, Manasse, and Slaman and Chisholm and
with previous work of Ash, Knight, and Slaman on uniformity in a
general computable structure-theoretical setting.