## Week 10, 17 March 2014 (16:00-18:00, 52 Pritchatts Road LT1)

### Walter Dean (Warwick)

Title: A brief history of Weak König's Lemma

Abstract: Weak König’s Lemma [$$\textrm{WKL}$$] states that every infinite binary tree has an infinite path. The theory $$\textrm{WKL}_0$$ results from adjoining the formalization of $$\textrm{WKL}$$ in the language of second order arithmetic to $$\textrm{RCA}_0$$ — i.e. the standard base theory employed in Reverse Mathematics consisting of induction for $$\Sigma^0_1$$-formulas and comprehension for $$\Delta^0_1$$-formulas. The goal of this talk will be to highlight several philosophical and methodological questions about Reverse Mathematics which pertain to the status of $$\textrm{WKL}$$ relative to traditional foundational programs. Many of these are related to the context in which this principle was first isolated (respectively by Kleene and Scott) with respect to the completeness of intuitionistic first-order logic and models of Peano arithmetic. This is part of joint work with Sean Walsh (UC Irvine).

The Midlands Logic Seminar was founded in 2011 and aims to cover all areas of mathematical logic, as well as related areas of theoretical computer science and philosophy of mathematics.

#### Logistics

All meetings for Term 2, 2014-15 will be Tuesday from 16:00-18:00 in room LT1, 52 Pritchatts Road on the campus of the University of Birmingham.
• campus map
To get to campus, take the train from Birmingham New Street to the University stop (7 minutes).

#### Organizers

Dr Richard Kaye
School of Mathematics
University of Birmingham

http://web.mat.bham.ac.uk/R.W.Kaye/

Dr Walter Dean
Department of Philosophy
University of Warwick

http://go.warwick.ac.uk/whdean