Rutgers Logic Seminar: Mondays

Information

Directions to the Hill Center can be found here. Please note that if you plan to drive, you will need a parking permit. This can be obtained from Hill 303, 305, or 307, though these offices close at 5:00 pm.

The

Seminar Schedule

5:00 pm - 6:00 pm, Room 705, Hill Center, Busch Campus

Past Talks

Abstract: I will discuss joint work with Su Gao, Steve Jackson, and Ed Krohne that proves that Z^2 has Borel chromatic number 3. Specifically, given any standard Borel space X and a free Borel action of Z^2 on X, one constructs a Borel graph on X by laying down a copy of the canonical (unmarked) Cayley graph of Z^2 on each Z^2-orbit. We prove that this graph always admits a graph-theoretic 3-coloring that is Borel.

Abstract: I will talk about mutually stationary sequences of sets. The notion of mutual stationarity, which was introduced by Foreman and Magidor in the 90s, has been developed as a notion of stationarity for subsets of singular cardinals and as means to address classical problems in infinitary combinatorics.

We will discuss the basic concepts and describe several known and recent results.

Abstract: The Ultrapower Axiom (UA) is a set theoretic principle that holds in all known canonical inner models, generalizing the linearity of the Mitchell order on normal ultrafilters to all countably complete ultrafilters. If UA can be refuted by any large cardinal axiom whatsoever, this rules out using anything like the current methodology to construct canonical inner models with even a single supercompact cardinal. Developing the theory of large cardinals assuming UA therefore leads to some insight into the inner model problem, and this talk will focus on two results in this theory: that GCH holds above the least supercompact cardinal, and that the least strongly compact cardinal is supercompact.

Abstract: The notion of forking gives a combinatorial notion of independence that makes sense in an arbitrary theory and simultaneously generalizes linear independence in vector spaces and algebraic independence in algebraically closed fields. Kim's thesis and subsequent work of Kim and Pillay developed the theory of forking in a simple theory and showed that simplicity may be characterized in several ways in terms of non-forking independence. In recent work in Itay Kaplan, we introduced Kim-independence, which corresponds to non-forking at a generic scale, and show that NSOP_1 theories may be understood in terms of this relation. In the talk, we will give an overview of the theory of Kim-independence and discuss the key examples.

Abstract: A well-known theorem of Mathias says that no infinite maximal almost disjoint, or "mad", family of infinite subsets of the natural numbers can be analytic. Mathias' proof utilizes a relationship between mad families and the "local" Ramsey theory of the natural numbers. We consider the analogous question for maximal almost disjoint families of infinite-dimensional subspaces of a countable, infinite-dimensional vector space, and connect it to the Ramsey theory of block sequences in such spaces, first developed by Gowers for Banach spaces.

Abstract: We introduce the concept of a twisted isomorphism, which is an isomorphism up to a permutation of the structure's language. We developed this concept in the course of proving results about metrically homogeneous graphs. This concept proved useful for partial classification results as well as finiteness results. The concept of a twist surprisingly is present in other work by Cameron and Tarzi, as well as by Bannai and Ito. We will discuss our results and their connections to other work.

Abstract: Say that consistently there are aleph_2 less than continuum graphs ! each of size aleph_1 which form a universal family. See work with Dzamonja [614] and [457]. Here we use a forcing which is half way between CS, product, and CS iteration. We also discuss the method in related cases. This talk is based on earlier results from paper [F1340] on the archive.

Abstract: Say that consistently there are aleph_2 less than continuum graphs ! each of size aleph_1 which form a universal family. See work with Dzamonja [614] and [457]. Here we use a forcing which is half way between CS, product, and CS iteration. We also discuss the method in related cases. This talk is based on earlier results from paper [F1340] on the archive.

Abstract: Say that consistently there are aleph_2 less than continuum graphs ! each of size aleph_1 which form a universal family. See work with Dzamonja [614] and [457]. Here we use a forcing which is half way between CS, product, and CS iteration. We also discuss the method in related cases. This talk is based on earlier results from paper [F1340] on the archive.

Abstract: As in the works with Maryanthe but for reduced power and the saturation is say for types consisting of atomic formulas. As it happen we get a different picture. This talk is based off of paper 1068 from the archive.

Needed knowledge: basic model theory.

Abstract: As in the works with Maryanthe but for reduced power and the saturation is say for types consisting of atomic formulas. As it happen we get a different picture. This talk is based off of paper 1068 from the archive.

Needed knowledge: basic model theory.

Abstract: As in the works with Maryanthe but for reduced power and the saturation is say for types consisting of atomic formulas. As it happen we get a different picture. This talk is based off of paper 1068 from the archive.

Needed knowledge: basic model theory.

Abstract: As in the works with Maryanthe but for reduced power and the saturation is say for types consisting of atomic formulas. As it happen we get a different picture. This talk is based off of paper 1068 from the archive.

Needed knowledge: basic model theory.

Abstract: As in the works with Maryanthe but for reduced power and the saturation is say for types consisting of atomic formulas. As it happen we get a different picture. This talk is based off of paper 1068 from the archive.

Needed knowledge: basic model theory.

Previous Semesters

Spring 2017

Fall 2016

Spring 2016