2009 seminar talk: Weak deteminacy, inductive operators and subsystems of analysis
Talk held by Philip Welch (University of Bristol) at the KGRC seminar on 2009-04-30.
It has been long known that the theory of Π11 and Σ11 monotone operators have links with Σ01 and Σ02 Determinacy respectively, and constructible ranks for strategies for such games have been found. In analysis the remaining Σ03 case (since by H Friedman Σ04 Determinacy is not provable in analysis) seems little investigated. We attempt to remedy this. We have in one version:
Δ13-CA0 << Σ03 Determinacy << Δ13-CA0 + a Σ13-absoluteness principle.
The above theorem is deliberately given in the spirit of weak subsystems of analysis; however we shall really be investigating low levels of the constructible hierarchy, and a concomitant notion of quasi-inductive operator.