On August 27, 1858, Italian mathematician and philosopher Giuseppe Peano was born. He is he author of over 200 books and papers, and is considered the founder of mathematical logic and set theory. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of consistency and completeness of number theory.
One of my collegaues called the other day and asked if we still relied on the distinction between intensional and extensional sets (really intensionally and extensionally defined sets). Yes, even more so now.
G. Friedman. (2008)cite http://arxiv.org/abs/0809.4221arxiv:0809.4221Comment: 57 pages, 32 figures. Further corrections and additions. Section 2 has been reorganized with new material added. Section 5.1 on Simplicial Hom added. Hopefully final version.
M. Bezem, T. Coquand, and S. Huber. 19th International Conference on Types for Proofs and Programs (TYPES 2013), volume 26 of Leibniz International Proceedings in Informatics (LIPIcs), page 107--128. Dagstuhl, Germany, Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, (2014)