# Welcome to New York Logic

Welcome to New York Logic!

Feb 13 Saturday Feb 14 Sunday Feb 15 Monday Feb 16 Tuesday Feb 17 Wednesday Feb 18 Thursday Feb 19 Friday

Set theory seminarFeb 19, 201610:00 am
Model theory seminarFeb 19, 201612:30 pm

go to the Calendar

## Upcoming talks and events:

Set theory seminarFriday, February 19, 201610:00 amGC 6417

# Why is Prikry forcing subcomplete?

Subcomplete forcing was introduced by Jensen as a class of forcings which do not add reals, but may change cofinalities to $\omega$, unlike proper forcing. In this talk I will show that Prikry forcing is subcomplete.

Model theory seminarFriday, February 19, 201612:30 pmGC 6417

# Lattices of Elementary Substructures

The set of elementary substructures of a model of PA, under the inclusion relation, form a lattice. The lattice problem for models of PA asks which lattices can be represented as substructure lattices of some model of PA. This question dates back to Gaifman’s work on minimal types, which showed that the two element chain can be represented as a substructure lattice. Since then, there have been many important contributions to this problem, including by Paris, Wilkie, Mills, and Schmerl, though no complete picture has yet emerged. Studying this question involves knowledge of models of PA as well as some nontrivial lattice theory and combinatorics. In my talk, I will survey some of the major results and, if there’s time, give an idea of the techniques used to study this question.

CUNY Logic WorkshopFriday, February 19, 20162:00 pmGC 6417

# The definability of radicals in noncommutative rings

College of Staten Island - CUNY

We will survey some results in the definability of radicals in rings, focusing on some recent results about noncommutative rings. In particular, we will show that there is no simple definition of the prime radical in the noncommutative setting, thus differentiating prime radicals in commutative/noncommutative rings.

Set theory seminarFriday, February 26, 201610:00 amGC 6417

# Title TBA

Kingsborough Community College, CUNY
CUNY Logic WorkshopFriday, February 26, 20162:00 pmGC 6417

# Title TBA

City Tech - CUNY
Set theory seminarFriday, March 4, 201610:00 amGC 6417

# Title TBA

City Tech - CUNY
Model theory seminarFriday, March 4, 201612:30 pmGC 6417

# Potential Cardinality for Countable First Order Theories

University of Maryland

Give a theory $T$, understanding the countable model theory of $T$ has long been a topic of research. The number of countable models of $T$ is a classical but very coarse invariant, and this was refined significantly by Friedman and Stanley with the notion of Borel reductions.

Given theories $T_1$ and $T_2$, it is often straightforward to show that $T_1$ is Borel reducible to $T_2$. However, there are few tools to show that no such Borel reduction exists. Most of the existing tools only work when the isomorphism relation of one or both is particularly simple, or at least Borel.

We define the notion of “potential cardinality” of $T$, denoted $|T|$, as the number of formally consistent, possibly uncountable Scott sentences which imply $T$. It turns out that if $T_1$ Borel reduces to $T_2$, then $|T_1|$ is less than or equal to $|T_2|$. Additionally, it turns out that very frequently, $|T|$ can be computed and is not a proper class.

We use this idea to give a new class of examples of first-order theories whose isomorphism relations are neither Borel nor Borel complete. Along the way we answer an old question of Koerwien and new question of Laskowski and Shelah.

This is joint work with Douglas Ulrich and Chris Laskowski.

Friday, March 11, 20169:00 am

# Set Theory Day March 11, 2016 at GC

GC 4102 (Science Center)

We announce a one-day conference, Set Theory Day on Friday, March 11, 2016, in celebration of the 50th birthday of Prof. Joel David Hamkins. The conference will take place at the CUNY Graduate Center and will last all day, with many of Prof. Hamkins’s former students giving talks on their work. All interested mathematicians are invited to attend. Further details will be posted here on nylogic.org as they become available.

Set theory seminarFriday, March 18, 201610:00 amGC 6417

# wPFA

University of Münster

We isolate a new forcing axiom, ${\rm wPFA}$, which is strictly between ${\rm BPFA}$ and ${\rm PFA}$. ${\rm wPFA}$ is equiconsistent with a remarkable cardinal, it implies the failure of $\square_{\omega_1}$, but it is compatible with $\square_\kappa$ for all $\kappa \geq \omega_2$. This is part of joint work with J. Bagaria and V. Gitman.

CUNY Logic WorkshopFriday, March 18, 20162:00 pmGC 6417

# Title TBA

Friday, March 25, 2016

# No talks March 25

Friday, March 25 is a CUNY holiday, for Good Friday, and so there will be no talks that day.

Set theory seminarFriday, April 1, 201610:00 amGC 6417

# Title TBA

CUNY Borough of Manhattan Community College
CUNY Logic WorkshopFriday, April 1, 20162:00 pmGC 6417

# Title TBA

Rutgers University
NERDS: New England Recursion & Definability SeminarSaturday, April 2, 2016

# NERDS on April 2, 2016

Springfield College

The Spring 2016 New England Recursion and Definability Seminar (“NERDS”) will take place on Saturday, April 2, 2016 at Springfield College, in Springfield, MA. Further details and abstracts of talks will be posted on nylogic.org as they become available.

Set theory seminarFriday, April 8, 201610:00 amGC 6417

# Title TBA

University of Illinois at Chicago
Set theory seminarFriday, April 15, 201610:00 amGC 6417

# Title TBA

University of California, Berkeley
Friday, April 29, 2016

# Spring break April 22 & 29

CUNY’s spring break includes both Friday, April 22 and Friday, April 29, and so there will be no talks those days.

Set theory seminarFriday, May 6, 201610:00 amGC 6417

# Title TBA

Kurt Godel Research Center
CUNY Logic WorkshopFriday, May 6, 20162:00 pmGC 6417

# Title TBA

Kurt Godel Research Center