New applications of Pták's extension theorem to weak compactness

Ultraproducts, the Compactness Theorem and Applications

This is a set of lecture notes used in a course on model theory at Virginia Commonwealth University (Math 591 Topics: Logic and Mathematical Structures), which I taught jointly with Sean Cox in the spring of 2014. Most of the material contained in these notes can be found in the following sources. References: • Chang and Keisler. Model Theory, Studies in Logic and the Foundations of Mathematics...

Applications of Hamilton’s Compactness Theorem for Ricci flow

1 Contents Applications of Hamilton's Compactness Theorem for Ricci flow Peter Topping 1 Applications of Hamilton's Compactness Theorem for Ricci flow 3 Overview 3 Background reading 4 Lecture 1. Ricci flow basics – existence and singularities 5 1.1. Initial PDE remarks 5 1.2. Basic Ricci flow theory 6 Lecture 2. Cheeger-Gromov convergence and Hamilton's compactness theorem 9 2.1. Convergence a...

Weak Compactness of the Set of ε-Extensions

Some Applications of Ball’s Extension Theorem

We present two applications Ball’s extension theorem. First we observe that Ball’s extension theorem, together with the recent solution of Ball’s Markov type 2 problem due to Naor, Peres, Schramm and Sheffilield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Secondly, we prove that the distortion required to embed the integer lattice {0, 1, . ...

On Compactness Theorem

In this talk we investigate the compactness theorem (as a property) in non-classical logics. We focus on the following problems: (a) What kind of semantics make a logic having compactnesss theorem? (b) What is the relationship between the compactness theorem and the classical model existence theorem (CME)/model existence theorem?