Contents Preface ix Notation xi Chapter 13. Filters and Ideals in Partial Orders 1 13.1. The general concept of a filter 1 13.2. Ultraproducts 8 13.3. A first look at Boolean algebras 12 Mathographical Remarks 24 Chapter 14. Trees 27 Mathographical Remarks 48 Chapter 15. A Little Ramsey Theory 49 Mathographical Remarks 65 Chapter 16. The A-System Lemma 67 Chapter 17. Applications of the Continuum Hypothesis 71 17.1. Applications to Lebesgue measure and Baire category 71 17.2. Miscellaneous applications of CH 79 Mathographical Remarks 85 Chapter 18. From the Rasiowa-Sikorski Lemma to Martin's Axiom 87 Mathographical Remarks 94 Chapter 19. Martin's Axiom 95 19.1. MA essentials 95 19.2. MA and cardinal invariants of the continuum 102 19.3. Ultrafilters on a 110 Mathographical Remarks 116 Chapter 20. Hausdorff Gaps 117 Mathographical Remarks 122 Chapter 21. Closed Unbounded Sets and Stationary Sets 123 21.1. Closed unbounded and stationary sets of ordinals 123 21.2. Closed unbounded and stationary subsets of [X]K1 131 Chapter 22. The -principle 139 Mathographical Remarks 146
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