Table of Contents
Introduction vi
Preliminaries 1
Forcing and Classifying Topoi 11
1.1. Category of Forcing Conditions as a Category of Models 11
1.2. Partially Ordered Sets vs. Distributive Lattices 17
More Geometric Forcing: Continuous Actions 27
2.1. On Infinite Sets 28
2.2. A Generic Dense Linear Ordering 31
2.3. Separable Closure of a Field 33
Forcing in SetTheory 37
3.1. 11-topology 37
3.2. Fibred Categories and Iterated Forcing 45
Applications to Intuitionistic Theories 62
4.1. Classifying Infinite Sequences 62
4.2. Spoiling Local Compactness of theReals 70
4.3. Making Baire Space Subcountable 77
4.4. Independence of Bar Induction in thePresence of
Continuity Principles 8 3
References 8 9
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