# Mathematical Sciences Research Institute

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# Seminar

DDC Junior Seminar: Semi-retractions and generalized indiscernibles in model theory September 08, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program: Decidability, definability and computability in number theory: Part 1 - Virtual Semester MSRI: Online/Virtual
Speaker(s) Lynn Scow (California State University, San Bernardino)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

The seminar will feature research talks by the six postdoctoral scholars appointed to the Fall 2020 DDC program, along with talks by students and other pre-tenure researchers associated with this program.  Since seminar attendees will have disparate backgrounds, we plan that these talks will not be too advanced, nor will they assume substantial background knowledge.  Our postdocs include number theorists, model theorists, and computable structure theorists, and talks can be expected to span all of these areas.

Video

#### Semi-Retractions And Generalized Indiscernibles In Model Theory

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

In this talk I will give an introduction to generalized indiscernible sequences and some of their uses in model theory. A generalized indiscernible sequence is an injective map $f: I \rightarrow M^n$ for some $n \geq 1$, where $I$ and $M$ are structures in possibly different signatures, and, moreover, same-length finite tuples $\overline{i}, \overline{j}$ that are indistinguishable by quantifier-free definable relations in $I$ map to $f(\overline{i}), f(\overline{j})$ that are indistinguishable by definable relations in $M$. Generalized indiscernible sequences both inherit some of their properties from results in generalized Ramsey theory, and serve to explicate some of these results. I will introduce a notion related to a (model-theoretic) reduct called a semi-retraction'' and talk about some consequences in generalized Ramsey theory.

#### Semi-Retractions And Generalized Indiscernibles In Model Theory

 H.264 Video 25149_28647_8493_Semi-Retractions_and_Generalized_Indiscernibles_in_Model_Theory.mp4