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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?

Dana Scott

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

Angus Macintyre

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

Solomon Feferman

Date: 13th March 2008

About the speaker: an ex-student of Alfred Tarski, Sol Feferman received the Rolf Schock Prize in Logic and Philosophy for 2003, is an ex-President of the ASL, and is Editor-in-Chief of the Gödel Collected Works.