Logic List Mailing Archive

Cross-Alps Logic Seminar Special Session, Virtual, 13 Jan 2022 [WLD 2022 Event]

On *Thursday 13th January* at *17.00* (CET), on the occasion of World Logic
Day 2022 <http://wld.cipsh.international/wld2022.html>, a special session
of the Cross-Alps Logic Seminars will take place, with special guest

*Menachem Magidor* (Hebrew University of Jerusalem)

*Title*: Sets of reals are not created equal: regularity properties of
subsets of the reals and other Polish spaces.

*Abstract*: A ?pathological set? can be a non measurable set, a set which
does not have the property of Baire (namely it is not a Borel set modulo a
first category set). A subset $A \subseteq P^{\omega}(\mathbb{N})$ (= the
infinite subsets of natural numbers) can be considered to be ?pathological?
if it is a counterexample to infinitary Ramsey theorem. Namely there does
not exist an infinite set of natural numbers such that all its subsets are
in our sets or all its infinite subsets are not in the set. A subset of the
Baire space $A\subseteq \mathbb{N}^{\mathbb{N}}$ can be considered to be
?pathological? if the infinite game $G_A$ is not determined. The game $G_A$
is an infinite game where two players alternate picking natural numbers,
forming an infinite sequence, namely a member of $\mathbb{N}^{\mathbb{N}}$.
The first player wins the round if the resulting sequence is in $A$. The
game is determined if one of the players has a winning strategy.
A prevailing paradigm in Descriptive Set Theory is that sets that have a
?simple description? should not be pathological. Evidence for this maxim is
the fact that Borel sets are not pathological in any of the senses
described above.In these talks we shall present a notion of ?super
regularity? for subsets of a Polish space, the family of universally Baire
sets. This family of sets generalizes the family of Borel sets and forms a
$\sigma$-algebra. We shall survey some regularity properties of universally
Baire sets , such as their measurability with respect to any regular Borel
measure, the fact that they have an infinitary Ramsey property etc. Some of
these theorems will require assuming some strong axioms of infinity. Most
of the talk should be accessible to a general Mathematical audience, but in
the second part we shall survey some newer results.

The event will stream on the Webex platform. Please write to  luca.mottoros
[at] unito.it  for the link to the event.

Menachem Magidor is an Israeli mathematician, specializing in set theory.
He served as President of the Association of Symbolic Logic (1996-1998), as
President of the Hebrew University of Jerusalem, and he was president of
the Division of Logic Methodology and Philosophy of Science and Technology
of the International Union of History and Philosophy of Science and
Technology. He won the Solomon Bublick Award in 2018.
He greatly contributed to the study of cardinals, forcing axioms,
infinitary logic, and saturated ideals. He is also active in the study of
non-monotonic logic and its application to Artificial Intelligence.

The Cross-Alps Logic Seminars is a series of seminars on mathematical
logic, organized by the logic groups of the universities of Genoa,
Lausanne, Turin and Udine. More information here

Luca Motto Ros
Università degli Studi di Torino
Dipartimento di Matematica
via Carlo Alberto, 10 - 10123 Torino, Italy

e-mail: luca.mottoros@unito.it
webpage: https://sites.google.com/site/lucamottoros/home?authuser=0
office phone: (+39) 011 670 2892
fax: (+39) 011 670 2878
[LOGIC] mailing list
Archive: http://www.illc.uva.nl/LogicList/

provided by a collaboration of the DVMLG, the Maths Departments in Bonn and Hamburg, and the ILLC at the Universiteit van Amsterdam