John Gregory showed (in 1970) that for a countable admissible set \(A\), if \(T\) is set of \(L_A\) sentences that is \(\Sigma_1\) on \(A\) and \(T\) has models \(\mathcalM\) and \(\mathcalN\) such that \(\mathcalN\) is a proper \(L_A\)-elementary extension of \(\mathcalM\), then \(T\) has an uncountable model. I will describe an example showing that the result fails if we drop the assumption that \(T\) is \(\Sigma_1\) on \(A\). This is joint work with my three current students, Jesse Johnson, Victor Ocasio, and Steven VanDenDriessche. The construction involves iterated forcing.
An example illustrating a theorem of Gregory
11.07.2012 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25