Mathematical Logic

  1. Proof Theory
    1. Structural Proof Theory
      1. Analysis of Sequent Calculus
        1. Structure and Rules
          1. Invertibility of Rules
            1. Admissibility
            2. Gentzen's Cut-Elimination Theorem
              1. Statement and Proof Outline
                1. Consequences for Proof Structure
                  1. Normalization
                  2. Subformula Property
                    1. Definition and Applications
                      1. Analytic Proofs
                      2. Applications of Cut-Elimination
                        1. Consistency Proofs
                          1. Interpolation Theorems
                            1. Decidability Results
                          2. Ordinal Analysis
                            1. Assigning Ordinals to Proofs
                              1. Ordinal Notations
                                1. Proof-Theoretic Ordinals
                                  1. Ordinal Bounds
                                  2. Gentzen's Consistency Proof for Peano Arithmetic
                                    1. Outline of the Proof
                                      1. Transfinite Induction
                                        1. Significance for Hilbert's Program
                                      2. Proof Complexity
                                        1. Measuring Proof Length
                                          1. Lower Bounds
                                            1. Propositional Proof Systems

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                                          9. Modal Logic