# Topic Archive: omega one like

Set theory seminarFriday, October 11, 201310:00 amGC 6417

# Embeddings among the $\omega_1$-like models of set theory, part II

The City University of New York

The speaker will give the second part of her talk, continued from the previous week. An $\omega_1$-like model of set theory is an uncountable model, all of whose initial segments are countable. The speaker will present two $\omega_1$-like models of set theory, constructed using $\Diamond$, which are incomparable with respect to embeddability: neither is isomorphic to a submodel of the other. Under a suitable large cardinal assumption, there are such models that are well-founded.