Wednesday, September 28, 20166:30 pmModels of PAGC 4214-03

# Ramsey Quantifiers and PA$(Q^2)$, part II

## Athar Abdul-Quader

### The CUNY Graduate Center

In this talk, I will discuss the relationship between “strong” models of PA($Q^2$) and $kappa$-like models. Namely, if $kappa$ is a regular uncountable cardinal, then every countable “weak” model has a $kappa$-like ($Q^2$)-elementary end extension that is a kappa like strong model, and if M is a strong model it is $kappa$ like for some $kappa$.