Tuesdays and Thursdays 10:00am–11:15am in South College E301

The section numbers in the schedule below come from the “Clean Version”, Revision 1802995, dated 2019-08-24, but new versions are posted often. I hope eventually to create my own “remix” of this book, but it is unlikely I will do so this semester.

The two exams will be

There are one or two homework exercises assigned nearly every class: a total of 32. The actual assignments are found scattered in the lecture notes, alongside the material they involve. Assigned exercises will be collected in four “bundles”:

*Bundle 1 (HW1–8)*is due*Th September 26th**Bundle 2 (HW9–15)*is due*Tu October 22nd*with*Exam 1**Bundle 3 (HW16–26)*is due*Tu November 19th**Bundle 4 (HW27–32)*is due*Th December 19th*with*Exam 2*

*Warning!* Everything about this schedule can and will change.

Date | Material (lecture notes pages) | Book sections | Homework |
---|---|---|---|

Tu 3 Sept | Course introduction | ||

Th 5 Sept | Metatheory, set theory (pp. 1–3) | §§1.1–4.6 | HW1 |

Tu 10 Sept | Mathematical induction, propositional logic (pp. 4–6) | §§5.1–5.5; §§54.1–54.5 | HW2, HW3 |

Th 12 Sept | Syntax/semantics of first-order logic (pp. 7–11) | §§12.1–12.12 | HW4, HW5 |

Tu 17 Sept | More on semantics of first-order logic (pp. 12–13) | §§12.13–12.14; §§14.1–14.5 | HW6, HW7 |

Th 19 Sept | Tableaux for first-order logic (pp. 13–15) | §§17.1–17.6 | HW8 |

Tu 24 Sept | Axiomatic deductions (pp. 16–20) | §§18.1–18.6 | HW9, HW10 |

Th 26 Sept | Deduction theorem and corollaries (pp. 20–22) HW 1–8 due |
§§18.7–18.11 | HW11 |

Tu 1 Oct | Soundness and consistency (pp. 23–25) | §18.12; §§30.1–30.2 | HW12 |

Th 3 Oct | Lemmas for completeness (pp. 25–30) | §§19.1–19.6 | HW13 |

Tu 8 Oct | Completeness, compactness (pp. 30–31) | §§19.8–19.11 | HW14 |

Th 10 Oct | Identity logic (pp. 31–34) | §18.13; §19.7 | HW15 |

Tu 15 Oct | No class. Monday class schedule. |
||

Th 17 Oct | Unit 1 review and questions. | ||

Tu 22 Oct | Theories; Peano and Robinson arithmetics (pp. 35–38)Exam 1 and HW 9–15 due. |
§§13.1–13.3; 29.1–29.4 | HW16, HW17 |

Th 24 Oct | Naïve foundations (pp. 39–40) | §1.6 | HW18 |

Tu 29 Oct | Numerals; Q vs. PA (pp. 40–45) |
§31.1; §31.5 | HW19 |

Th 31 Oct | Recursive functions (pp. 45–49) | §§25.1–25.7 | HW20, HW21 |

Tu 5 Nov | More on recursive functions (pp. 49–52) | §§25.8–25.13 | HW22, HW23 |

Th 7 Nov | Representing functions in Q (pp. 52–56) |
§31.6–31.9 | HW24, HW25 |

Tu 12 Nov | Representing recursion (pp. 56–59) | §§31.3–31.4 | HW26 |

Th 14 Nov | Arithmetization of syntax (pp. 59–64) | §§30.3–30.5; §30.8; §31.2 | HW27, HW28 |

Tu 19 Nov | Fixed point theorem; Gödel’s first theorem (pp. 64–69)HW 16–26 due. |
§§33.1–33.3 | HW29 |

Th 21 Nov | Gödel-Rosser and Gödel’s second theorem (pp. 69–72) | §§33.4–33.7 | HW30 |

24–30 Nov | No class. Thanksgiving break. |
||

Tu 3 Dec | Löb’s theorem; Tarski’s theorem (pp. 72–74) | §§33.8–33.9 | HW31 |

Th 5 Dec | Recursive undecidability (pp. 74–77) | §31.10; §32.4; §32.9 | HW32 |

Tu 10 Dec | Unit 2 review and questions. | ||

Th 19 Dec | End of finals week.Exam 2 and HW 27–32 due. |