2015-03-11: Peter Hancock

Sat, 21 Oct 2023 21:24:08 +0100

Peter Hancock

Collapsing

Abstract

The topic comes from theory of infinitary proofs, and cut-elimination. In essence it is about nicely-behaved maps from higher "infinities" to lower ones, as the infinitary proofs are er, infinite, and can be thought of as glorified transfinite iterators. What might nice behaviour mean?

You can think of it as how to fit an uncountable amount of beer into a bladder whose capacity is merely countable. (Or maybe even finite.)

The most ubiquitous form of infinity is the regular cardinal, iepassing from a container F to F + (mu F -> _), where mu is the W-type operation. I'll "explain" regular collapsing as being all about diagonalisation.

2015-03-11 11:00:00 UTC
LT1310