8th Meeting on
Contemporary Mathematics
February 17-19, 2018

 School of Mathematics IPM All Meetings 

توجه !!
این همایش در زمان اعلام شده برگزار نمی‌شود.

This event has been canceled.

W. Hugh Woodin
(Harvard University)

Ultimate L


The modern mathematical study of infinity began in the period 1879-84 with a series of papers by Cantor that defined the fundamental framework of the subject. Within 40 years the key ZFC axioms for Set Theory were in place and the stage was set for the detailed development of transfinite mathematics, or so it seemed. However, in a completely unexpected development, Cohen showed in 1963 that even the most basic problem of Set Theory, that of Cantor's Continuum Hypothesis, was not solvable on the basis of the ZFC axioms.

The 50 years since Cohen's announcement has seen a vast development of Cohen's method and the realization that the occurrence of unsolvable problems is ubiquitous in Set Theory. This arguably challenges the very conception of Cantor on which Set Theory is based.
However, during this same period, the detailed study of special cases of the Continuum Hypothesis led to a remarkable success. This was the discovery and validation of the determinacy axioms for Second Order Number Theory. The resulting theory is largely immune to Cohen’s method.

Almost 25 years before Cohen’s discovery of forcing, Gödel discovered the Constructible Universe of Sets and defined the axiom "V = L” which is the axiom that asserts that every set is constructible. This axiom implies the Continuum Hypothesis and more importantly, Cohen’s method of forcing cannot be used in the context of the axiom "V = L”. However the axiom "V = L" is false since it limits the fundamental nature of infinity. In particular the axiom refutes (most) strong axioms of infinity and it refutes the determinacy axioms of Second Order Number Theory.

A key question emerges. Is there an “ultimate” version of Gödel’s constructible universe yielding an axiom "V = Ultimate L" which retains the power of the axiom "V = L" for resolving questions like that of the Continuum Hypothesis, which is also immune against Cohen’s method of forcing, and yet which does not refute strong axioms of infinity? Such an axiom would necessarily provide the generalization of the determinacy axioms of Second Order Number Theory to the entire universe of sets.

Until recently there seemed to be a number of convincing arguments as to why no such ultimate L can possibly exist. But the situation is now changed.

Feb. 17

1st Lecture Coffee Break
2nd Lecture
Feb. 18

3rd Lecture Coffee Break Public Lecture

Location: Lecture Hall 1, IPM Niavaran Building,
Niavaran Square, Tehran
The attendance is free, but requires registration.
Please fill out the registration form and
send it to  gt@ipm.ir  with the subject "MCM".

School of Mathematics,
IPM - Institute for Research in Fundamental Sciences
Niavaran Building, Niavaran Square, Tehran, Iran
Tel: +98 21 222 90 928
E. Eftekhary
M. Golshani
M. Nassiri