| Time: | 12 - 1:20 p.m. |
| Room: |
Baker Hall 150
|
| Speaker: | Dana Scott Hillman University Professor Departments of Computer Science, Philosophy and Mathematical Sciences Carnegie Mellon University |
| Title: |
Parametric sets and virtual classes
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| Abstract: |
In an axiomatic development of geometry, there is much
convenience to be found in treating various loci as sets. Thus, a line
corresponds to the set of all points lying on the line; a circle, to the
set of all points on the circumference. Moreover, sets of sets are
natural, say in considering pencils of lines or circles or conics. And
families of pencils are used as well. Does geometry need a full set
theory, therefore? In giving a negative answer, we shall consider
higher-type sets introduced by parametric definitions with just finite
lists of points as parameters. An attempt will be made at axiomatizing
such sets together with a notation for virtual classes. The objective is
to have the use of set-theoretical notations without the ontology of
higher-type logic and Zermelo-Fraenkel set theory.
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