Computability learning seminar

Speaker

Matthew Harrison-Trainor, Department of Pure Mathematics, University of Waterloo

Forcing and atomic models abstract

The theorem AMT says that if T is an atomic theory, then T has an atomic model. We will introduce forcing to give a conservation result over RCA_0: AMT is restricted \PI^1_2-conservative over RCA_0, that is, any sentence of the form ∀ A(Ω(A) → ∃BΦ(A, B)), where Ω is arithmetic and Φ is Σ^0_3, provable by AMT is already provable in RCA_0. In particular, this will show that AMT does not prove WKL_0, RT^2_2, and a number of other principles.