Modified bar recursion

Bar Recursion and Products of Selection Functions

We show how two iterated products of selection functions can both be used in conjunction with system T to interpret, via the dialectica interpretation and modified realizability, full classical analysis. We also show that one iterated product is equivalent over system T to Spector’s bar recursion, whereas the other is T-equivalent to modified bar recursion. Modified bar recursion itself is show...

Modified Bar Recursion and Classical Dependent Choice

Abstracts of the invited speakers

s of the invited speakers Dag Normann, University of Oslo, Norway Revisiting Transfinite Types In this talk I will reconstruct spaces of countable and uncountable transfinite types, this time using limit spaces. This approach turns out to give a better access to internal concepts of computability for such spaces. The talk will be a report on ongoing research. This research is rooted in earlier ...

The equivalence of bar recursion and open recursion

Several extensions of Gödel’s system T with new forms of recursion have been designed for the purpose of giving a computational interpretation to classical analysis. One can organise many of these extensions into two groups: those based on bar recursion, which include Spector’s original bar recursion, modified bar recursion and the more recent products of selections functions, or those based on...

On Bar Recursion and Choice in a Classical Setting

We show how Modified Bar-Recursion, a variant of Spector’sBar-Recursion due to Berger and Oliva can be used to realize the Axiomof Choice in Parigot’s Lambda-Mu-calculus, a direct-style language forthe representation and evaluation of classical proofs.We rely on Hyland-Ong innocent games. They provide a model to per-form the usual infinitary reasoning on Bar-Recursion needed...