**September 9**

Saeideh Bahrami,
Institute for Research in Fundamental Sciences, Tehran

**Fixed Points of Initial Self-Embeddings of Models of Arithmetic**

In 1973, Harvey Friedman proved his striking result on *initial self-embeddings* of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of $ \mathrm{PA} $, to results about the fixed point set of initial self-embeddings of countable nonstandard models of $ \mathrm{I}\Sigma_{1} $.