# The Löb Lecture

## Prof. Justin Moore (Cornell University)

What makes the continuum $\aleph_2$

**Date:** 14th April 2023, 16:00 – MALL (School of Mathematics)

**Slides (PDF)** **Recording**

While historically the question has been whether the Continuum Hypothesis is true or false, determining the relationship between the continuum and $\aleph_2$ (the second uncountable cardinal) is arguably a much deeper and more interesting mathematical problem. I will lay out a philosophical and mathematical argument for why $\aleph_2$ is the right value for the continuum.

**Related talks** – in MALL (School of Mathematics)

Justin Moore Ordinal arithmetic and subgroups of Thompson's group, Thursday 13th April, 14:00

Asaf Karagila (Leeds) What, why, and how are Forcing Axioms?, Friday 14th April, 14:00

Interview of Justin Moore by Steven Strogatz (19th April): How Can Some Infinities Be Bigger Than Others?

## Prof. Em. Dana Scott (Carnegie-Mellon & Berkeley)

Why Mathematical Proof?

**Date:** 18th May 2016, 16:30 – Roger Stevens Lecture Theatre 24

**Slides (PDF)**

Mathematicians (and school children) have been giving proofs for millennia. Why?

Why are they needed? How formal should proofs be? Are there different systems/philosophies for

organizing proofs? Are axioms always "self-evident"? Will new axioms for Mathematics be proposed? Will computers eventually take over the drudgery? Will this lecture make you worry?

**About the speaker:** a Turing Award-winner and recipient of many other international awards, Professor Scott is a highly distinguished mathematical logician who, in a long career, has made fundamental contributions to set theory, model theory and the theory of computation.

## Prof. Angus Macintyre (QMUL)

Logic and Arithmetic: Models, Definitions, Proofs

**Date:** 18th January 2012

Since 1930 (when Herbrand and Skolem were working both on logic and number theory) there has been a lot of activity on models of arithmetic, complexity of definitions of arithmetic notions, and the strength of various axiom systems for arithmetic. I will survey the achievements, challenges and failures of this activity.

**About the speaker:** Prof. Macintyre is a world-leading logician, and an engrossing speaker who has a wide engagement with mathematics.

## Prof. Solomon Feferman (Stanford)

Gödel, Nagel, Minds and Machines