Topics In Model Theory

Anand Pillay (Univ Of Notre Dame, Usa)

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English

World Scientific Publishing Co Pte Ltd
26 April 2024

Mathematical logic

Summary
Details

The book has two chapters. The first chapter is a modern or contemporary account of stability theory. After a preliminary section on some of the basic techniques of model theory, the focus is on local (formula-by-formula) stability theory, treated a little differently from in the author's Geometric Stability Theory book. There is also a survey of general and geometric stability theory, as well as detailed applications to combinatorics (regularity lemma) using pseudofinite methods.

The second chapter is an introduction to 'continuous logic' or 'continuous model theory', where truth values are real numbers, drawing on the main texts and papers, but with an independent point of view. This chapter also includes some historical background, a discussion of hyperimaginaries in classical first order model theory, as well as an introduction to local stability in the continuous framework making use of some functional analysis results from Grothendieck's thesis.

These chapters are based on notes, written by students, from a couple of advanced graduate courses in Notre Dame, in Autumn 2018, and Spring 2021.

By: Anand Pillay (Univ Of Notre Dame Usa)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
ISBN: 9789811243998
ISBN 10: 9811243999
Pages: 150
Publication Date: 26 April 2024
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active