Mathematical Logic

  1. Computability Theory
    1. Informal Notion of Algorithm
      1. Historical Context
        1. Intuitive Definition
          1. Effective Procedures
          2. Formal Models of Computation
            1. Turing Machines
              1. Definition and Operation
                1. Configurations and Computations
                  1. Acceptance and Rejection
                    1. Universal Turing Machine
                      1. Variants of Turing Machines
                      2. Recursive Functions
                        1. Primitive Recursive Functions
                          1. Definition and Examples
                            1. Closure Properties
                            2. μ-Recursive Functions
                              1. Definition and Examples
                                1. Minimization Operator
                              2. Lambda Calculus
                                1. Syntax and Reduction Rules
                                  1. Church Numerals
                                    1. Expressiveness
                                    2. Register Machines
                                      1. Post Systems
                                      2. The Church-Turing Thesis
                                        1. Statement and Interpretations
                                          1. Evidence Supporting the Thesis
                                            1. Limitations and Criticisms
                                            2. Decidability and Undecidability
                                              1. Decidable Problems
                                                1. Definition and Examples
                                                  1. Decision Procedures
                                                  2. Undecidable Problems
                                                    1. Definition and Examples
                                                      1. Proof Techniques
                                                      2. The Halting Problem
                                                        1. Statement and Proof of Undecidability
                                                          1. Variants and Applications
                                                          2. Reducibility
                                                            1. Many-One Reducibility
                                                              1. Turing Reducibility
                                                                1. Degrees of Unsolvability
                                                              2. Rice's Theorem
                                                                1. Statement and Proof
                                                                  1. Limitations
                                                                  2. The Arithmetical Hierarchy
                                                                    1. Definition of the Hierarchy
                                                                      1. Σ₀, Π₀, and Δ₀ Classes
                                                                        1. Higher Levels of the Hierarchy
                                                                          1. Examples of Classification
                                                                            1. Post's Theorem

                                                                          Previous

                                                                          4. Model Theory

                                                                          Go to top

                                                                          Next

                                                                          6. Incompleteness Theorems