Kiddie Talk: Ultraproducts and Szeméredi’s Theorem

نویسنده

  • EVAN WARNER
چکیده

As promised, this talk will not assume any knowledge of ultrafilters, ultraproducts, or any model theory. The plan is as follows: (1) Ultrafilters (2) Ultraproducts (3) Joke (4) What are ultraproducts good for? (5) Szeméredi’s theorem via ultraproducts References: Mostly Terence Tao’s various blog notes on ultraproducts. For model theory, see David Marker’s Model Theory: An Introduction for a very readable exposition.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Ultraproducts and the Group Ring Semiprimitivity Problem

This expository paper is a slightly expanded version of the final talk I gave at the group rings conference celebrating the 25th anniversary of the Institute of Mathematics and Statistics at the University of São Paulo. The talk concerned an application of ultraproducts to the solution of the semiprimitivity problem for group algebras K[G] of locally finite groups G. It explained why the specia...

متن کامل

Compactness Theorem for Some Generalized Second-Order Language

For the first-order language the compactness theorem was proved by K. Gödel and A. I. Mal’cev in 1936. In 1955, it was proved by J. Łoś (1955) by means of the method of ultraproducts. Unfortunately, for the usual second-order language the compactness theorem does not hold. Moreover, the method of ultraproducts is also inapplicable to second-order models. A possible way out of this situation is ...

متن کامل

Model Theory and Hypergraph Regularity

1. Ultrafilters, ultraproducts and ultralimits 1 1.1. Filters and ultrafilters 1 1.2. Ultralimits 2 1.3. Some model-theoretic notation 3 1.4. Ultraproducts of first-order structures 3 1.5. References 6 2. Graph regularity and measures on ultraproducts 6 2.1. Szemerédi’s regularity lemma 6 2.2. Finitely additive measures 7 2.3. Obtaining countable additivity 9 2.4. Integration for charges (signe...

متن کامل

A Survey of Ultraproduct Constructions in General Topology

This survey is intended primarily for two readerships: general topologists who know a little model theory, and model theorists who know a little general topology. Both camps can boast a healthy constituency, and most of this paper should be readily accessible to anyone in either. The ultraproduct construction has a long and distinguished history. While its beginnings go back to the 1930s with K...

متن کامل

Institution-independent Ultraproducts

We generalise the ultraproducts method from conventional model theory to an institutionindependent (i.e. independent of the details of the actual logic formalised as an institution) framework based on a novel very general treatment of the semantics of some important concepts in logic, such as quantification, logical connectives, and ground atomic sentences. Unlike previous abstract model theore...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012