Vladimir Kanovei, Institute for Information Transmission Problems
On the significance of parameters in the choice and сomprehension schemata in the 2nd-order Peano arithmetic
Parameters are free variables in various axiom schemata in PA, ZFC, and other similar theories. Given an axiom schema S, we let S* be the parameter-free sub-schema.
Kreisel (A survey of proof theory, JSL 1968) was one of those who paid attention to the comparison of some schemata in second-order PA and their parameter-free versions. In particular, Kreisel noted that[...] if one is convinced of the significance of something like a given axiom schema, it is natural to study details, such as the effect of parameters.
This talk is devoted to the effect of parameters in the schemata of Comprehension and Choice in second-order arithmetic.