Mathematical Logic

  1. Axiomatic Set Theory
    1. The Role of Set Theory as a Foundation
      1. Sets as Fundamental Objects
        1. Set Theory and Other Branches of Mathematics
          1. Russell's Paradox and the Need for Axioms
          2. The Zermelo-Fraenkel Axioms
            1. Axiom of Extensionality
              1. Axiom of Empty Set
                1. Axiom of Pairing
                  1. Axiom of Union
                    1. Axiom of Power Set
                      1. Axiom of Infinity
                        1. Axiom Schema of Separation
                          1. Axiom Schema of Replacement
                            1. Axiom of Regularity
                              1. Cumulative Hierarchy of Sets
                              2. The Axiom of Choice
                                1. Statement of the Axiom
                                  1. ZFC System
                                    1. Equivalent Formulations
                                      1. Well-Ordering Principle
                                        1. Zorn's Lemma
                                          1. Hausdorff Maximal Principle
                                          2. Independence from ZF
                                            1. Consequences of Choice
                                            2. Ordinal and Cardinal Numbers
                                              1. Well-Orderings and Ordinals
                                                1. Definition and Properties
                                                  1. Ordinal Arithmetic
                                                    1. Transfinite Induction and Recursion
                                                    2. Cardinality and Cardinal Arithmetic
                                                      1. Comparing Cardinalities
                                                        1. Cardinal Arithmetic
                                                          1. Cofinality
                                                        2. The Continuum Hypothesis
                                                          1. Statement and Significance
                                                            1. Relation to Cardinal Numbers
                                                              1. Generalized Continuum Hypothesis
                                                              2. Independence Proofs and Forcing
                                                                1. Cohen's Method of Forcing
                                                                  1. Forcing Conditions
                                                                    1. Generic Extensions
                                                                      1. Independence of CH and AC
                                                                        1. Other Independence Results

                                                                      Previous

                                                                      6. Incompleteness Theorems

                                                                      Go to top

                                                                      Next

                                                                      8. Proof Theory