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

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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


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