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

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