Computability learning seminar

Matthew Harrison-Trainor
Pure Mathematics University of Waterloo

“Forcing and Atomic Models - Part 2”

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 RCA0: AMT is restricted Π12-conservative over RCA0, that is, any sentence of the form ∀A(Ω(A) → ∃BΦ(A, B)), where Ω is arithmetic and Φ is Σ03, provable by AMT is already provable in RCA0. In particular, this will show that AMT does not prove WKL0, RT2, and a number of other principles.

Please note the time.