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.
General
Imprint: |
World Scientific Publishing Co Pte Ltd
|
Country of origin: |
Singapore |
Release date: |
February 2024 |
Authors: |
Anand Pillay
|
Format: |
Hardcover
|
Pages: |
150 |
ISBN-13: |
978-981-12-4380-6 |
Categories: |
Books
|
LSN: |
981-12-4380-8 |
Barcode: |
9789811243806 |
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