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<title>World Logic Day at Fields Institute</title>
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<meta name="author" content="David Schrittesser">
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<h1>
<a href="http://www.fields.utoronto.ca/activities/21-22/set-theory-seminar">Set Theory Seminar</a> at <a href="http://www.fields.utoronto.ca/">Fields Institute</a> World Logic Day 2022 Talks
</h1>

<section>
<p>
January 14th is <a href="https://en.unesco.org/commemorations/worldlogicday"> World Logic Day</a> (as designated by the UNESCO).
</p>
<p>
On this day the Toronto Set Theory Seminar at Fields Institute will hold
a special session with 4 short talks (20 minutes each), showcasing recent
research by faculty and postdocs at University of Toronto.
</p>
<p><a href="https://wld.cipsh.international/wld2022.html">Here</a> is a list of further world logic day events around the world.
</p>

<h2>
Program
</h2>

<p>
<h3>
13:30
</h3>
<h4>
Ivan Ongay-Valverde and Franklin D. Tall<sup>&#65121;</sup>:
A New Topological Generalization of Descriptive Set Theory
</h4>
<p>
We generalize the K-analytic spaces to the K-&sigma;-projective spaces.
We get an application to Selection Principles:
</p>
<p>
<b>Theorem.</b> The Axiom of &sigma;-Projective Determinacy implies every
K-&sigma;-projective Menger space is Hurewicz.
</p>
</p>
<hr>
<p>
<h3>
13:50
</h3>
<h4>
Ivan Ongay Valverde<sup>&#65121;</sup> and Franklin D. Tall:
 Upper semi-continuous compact-valued functions and the K-sigma-projective hierarchy
</h4>
Completing the previous talk, we introduce USCCV functions (actually, multifunctions), which were employed in the study of K-analytic spaces, and show how to use them to prove the crucial:

<p>
<b>Theorem.</b> K-&sigma;-projective spaces are projectively &sigma;-projective.
</p>
</p>
<hr>
<p>
<h3>
14:10
</h3>
<h4>
Christopher J. Eagle, Clovis Hamel<sup>&#65121;</sup>, Sandra Müller, and Franklin D. Tall: An undecidable extension of Morley's theorem on the number of countable models
</h4>
Morley&#8217;s theorem states that the number of non-isomorphic countable models of a
complete countable first-order theory in a countable language is <span
class="cmsy-10">&#x2135;</span><sub><span
class="cmr-7">0</span></sub> or <span
class="cmsy-10">&#x2135;</span><sub><span
class="cmr-7">1</span></sub> or 2<sup><span
class="cmsy-7">&#x2135;</span><sub><span
class="cmr-5">0</span></sub></sup>.
Vaught&#8217;s conjecture remains one of the most important open problems in Model
Theory, asking whether <span
class="cmsy-10">&#x2135;</span><sub><span
class="cmr-7">1</span></sub> can be omitted in the conclusion of Morley&#8217;s theorem.
Even though Vaught&#8217;s conjecture is trivially false in second-order logic, no result was
known regarding Morley&#8217;s trichotomy for second-order logic. We shall show using
forcing, large cardinals and descriptive set theory that the second-order version of
Morley&#8217;s theorem is undecidable.
</p>
<hr>
<p>

<h3>
14:30
</h3>
<h4>
Andrew Marks and Spencer Unger<sup>&#65121;</sup>:
Flows on the torus
</h4>
In joint work with Andrew Marks, we gave a constructive solution to
Tarski's circle squaring problem.  In particular, we showed that a
disk and a square with the same area are equidecomposible using
translations.  One important innovation of the proof was to
construct a real valued flow from the disk to the square.  The notion
 of flow that we use comes from the study of networks and is related
to max flow-min cut.  In this talk, I will sketch a simpler
construction of a real-valued flow from the disk to the square, which
is joint work with Andrew Marks.  Using discrepancy estimates due to
Laczkovich, this argument works for sets whose boundary has small
upper Minkowski dimension.  I will also mention ongoing work with
Anton Bernshteyn and Anush Tserunyan where we construct a large and
diverse collection of flows under the same assumptions.

</p>
<hr>
<p>

<h3>
14:50
</h3>
<h4>Haosui Duanmu, David Schrittesser<sup>&#65121;</sup>, and William Weiss:
Infinitesimals and Probabilities
</h4>
In joint work with Haosui Duanmu and William Weiss, we investigate
applications of nonstandard analysis in measure theory. The use of
infinitesimals and hyperfinite probability spaces offers alternative
viewpoints on many classical problems, via Peter Loeb's construction
of measures using hyperfinite probability mass functions to construct
classical measures. In this talk, I will describe a solution to a
problem posed by Keisler, about Loeb measures, and also mention
applications in statistics which are joint work with Haosui Duanmu
and Daniel Roy.
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<h2>Contact</h2>
<p>
  email: david.schrittesser "at" univie.ac.at
</p>
<p><i>Page last changed: January 2021</i></p> </div>
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