Book:Winfried Just/Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician

Winfried Just and Martin Weese: Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician

Published $\text {1997}$, American Mathematical Society

ISBN 0-8218-0266-6

Subject Matter

• Set Theory

Contents

Preface

Notation

Chapter $13$. Filters and Ideals in Partial Orders

$13.1$ The general concept of a filter

$13.2$ Ultraproducts

$13.3$ A first look at Boolean algebras

Mathographical Remarks

Chapter $14$. Trees

Mathographical Remarks

Chapter $15$. A Little Ramsey Theory

Mathographical Remarks

Chapter $16$. The $\Delta$-System Lemma

Chapter $17$. Applications of the Continuum Hypothesis

$17.1$ Applications to Lebesgue measure and Baire category

$17.2$ Miscellaneous applications of CH

Mathographical Remarks

Chapter $18$. From the Rasiowa-Sikorski Lemma to Martin's Axiom

Mathographical Remarks

Chapter $19$. Martin's Axiom

$19.1$ MA essentials

$19.2$ MA and cardinal invariants of the continuum

$19.3$ Ultrafilters on $\omega$

Mathographical Remarks

Chapter $20$. Hausdorff Gaps

Mathographical Remarks

Chapter $21$. Closed Unbounded Sets and Stationary Sets

$21.1$ Closed unbounded and stationary sets of ordinals

$21.2$ Closed unbounded and stationary subsets of $\sqbrk X^{< \kappa}$

Chapter $22$. The $\diamond$-Principle

Mathographical Remarks

Chapter $23$. Measurable Cardinals

Mathographical Remarks

Chapter $24$. Elementary Submodels

$24.1$ Elementary facts about elementary submodels

$24.2$ Applications of elementary submodels in set theory

Mathographical Remarks

Chapter $25$. Boolean Algebras

Mathographical Remarks

Chapter $26$. Appendix: Some General Topology

Index

Index of Symbols