Summary: Tutorial: Generic Elementary Embeddings
Lecture 2: Consistency results
University of California, Irvine
We saw how generic elementary embedding as-
sumptions are natural generalizations of con-
ventional large cardinals.
We saw that they could naturally be charac-
terized by the "three parameters".
Finally, we saw that the combinatorial device
of "ideals" could be used to encode the generic
elementary embedding assumptions.
Induced vs. natural ideals
The manner we got ideals from generic em-
beddings was to start with a generic embed-
ding j : V M V [G], choose an element