Jindrich Zapletal Hinman Box 6188, Dartmouth College, Hanover NH 03755 zapletal@dartmouth.edu Title: Terminal notions in set theory Abstract: For certain notions currently in use in mathematics a thesis can be exactly formulated and proved saying that these notions cannot be split into finer subnotions. This involves proving some absoluteness theorems and a construction of some optimal models of set theory. It is a formal explanation of the fact that mathematicians intuitively consider some of these notions as optimal in a certain type of arguments. I will give several examples.