Fast track to forcing / Mirna Džamonja.

Format:

Book

Author/Creator:

Džamonja, Mirna, 1965- author.

Series:

London Mathematical Society student texts ; 98.

London Mathematical Society student texts ; 98

Language:

English

Subjects (All):

Forcing (Model theory).

Axiomatic set theory.

Physical Description:

xiii, 147 pages ; 23 cm.

Place of Publication:

Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2021.

Summary:

This quick yet detailed introduction to set theory and forcing builds the reader's intuition about it as much as the mathematical detail. Intuition, rather absent from the existing literature on the subject, here plays a large role. The reader will not only learn the facts, but will understand why they are true and will be brought to ask: what else could be true? Having presented forcing in Part I, the second part of the book discusses contemporary issues in the theory of forcing. It includes known and some previously unpublished results as well as many open questions. This is ideal for those who want to start a research career in forcing but do not have a personal interlocutor. Obviously, not everything about forcing is in this book. Many references are included to help the reader further explore the vast amount of research literature available on the subject.

Contents:

Axiomatic systems

Zermelo-Fraenkel axioms and the axiom of choice

Well orderings and ordinals

Cardinals

Models and independence

Some class models of ZFC

Forcing

Violating CH

Classical extensions

Iterated forcing and Martin's axiom

Some more large cardinals

Limitations of Martin's axiom and countable supports

Proper forcing and PFA

[aleph]2 and other successors of regulars

Singular cardinal hypothesis and some PCF

Forcing at singular cardinals and their successors.

Notes:

Includes bibliographical references and index.

Other Format:

Online version: Džamonja, Mirna. Fast Track to Forcing.

ISBN:

9781108420150

110842015X

9781108413145

1108413145

OCLC:

1158505302