A logical view at Tao's finitization of principles in analysis

Jaime Gaspar

In 2007 and 2008 Terence Tao wrote on his blog essays about the finitization of principles in analysis. His goal is to find for infinite qualitative ``soft analysis'' statements equivalent finitary quantitative ``hard analysis'' statements. These equivalences are usually proved using a contradiction and sequentially compactness argument. Tao's two prime examples are:

We take a logical look at Tao's essays and make mainly two points:

These points are then illustrated in a case study: the almost finitization of the infinite pigeonhole principle.

This is joint work with Ulrich Kohlenbach.