**Contemporary Mathematics**

Volume: 530;
2010;
200 pp;
Softcover

MSC: Primary 03; 05; 28;

Print ISBN: 978-0-8218-4833-3

Product Code: CONM/530

List Price: $73.00

Individual Member Price: $58.40

**Electronic ISBN: 978-0-8218-8209-2
Product Code: CONM/530.E**

List Price: $73.00

Individual Member Price: $58.40

# Ultrafilters across Mathematics

Share this page *Edited by *
*Vitaly Bergelson; Andreas Blass; Mauro Di Nasso; Renling Jin*

This volume originated from the International Congress
“ULTRAMATH: Applications of Ultrafilters and Ultraproducts in
Mathematics”, which was held in Pisa, Italy, from June
1–7, 2008.

The volume aims to present the state-of-the-art of applications in
the whole spectrum of mathematics which are grounded on the use of
ultrafilters and ultraproducts. It contains two general surveys on
ultrafilters in set theory and on the ultraproduct construction, as
well as papers that cover additive and combinatorial number theory,
nonstandard methods and stochastic differential equations, measure
theory, dynamics, Ramsey theory, algebra in the space of ultrafilters,
and large cardinals.

The papers are intended to be accessible and interesting for
mathematicians who are not experts on ultrafilters and
ultraproducts. Greater prominence has been given to results that can
be formulated and presented in non-special terms and be, in principle,
understandable by any mathematician, and to those results that connect
different areas of mathematics, revealing new facets of known
important topics.

#### Readership

Graduate students and research mathematicians interested in the theory of ultrafilters and ultraproducts..

# Table of Contents

## Ultrafilters across Mathematics

- Contents v6 free
- Preface vii8 free
- An Elementary Approach to Stochastic Differential Equations Using the Infinitesimals 112 free
- Ultrafilters, IP sets, Dynamics, and Combinatorial Number Theory 2334
- Ultrafilters and Set Theory 4960
- Measure-Centering Ultrafilters 7384
- Algebra in the Space of Ultrafilters and Ramsey Theory 121132
- Ultrapower of N and Density Problems 147158
- The Ultraproduct Construction 163174
- Ultrafilters and Large Cardinals 181192