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

The section numbers in the schedule below come from the “Clean Version”, Revision ec6994c, dated 2022-08-13, but new versions are posted often.

There are homework exercises assigned every class: a total of 36. 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 (HW 1–8)*is due*Thurs. September 29th**Bundle 2 (HW 9–17)*is due*Thurs. October 20th**Bundle 3 (HW 18–28)*is due*Thurs. November 17th**Bundle 4 (HW 29–36)*is due*Tues. December 20th*

You are also expected to attend class regularly, prepared to discuss the material, and participate by asking questions, making comments and responding to the questions and comments of others.

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

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

Tu 6 Sept | Course introduction | ||

Th 8 Sept | Metatheory, set theory (pp. 1–3) | §§1.1–4.9 | HW1 |

Tu 13 Sept | Mathematical induction, propositional logic (pp. 4–6) | §§71.1–71.5; §§7.1–7.5 | HW2, HW3 |

Th 15 Sept | Syntax/semantics of first-order logic (pp. 7–11) | §§15.1–15.8; §§16.1–16.3 | HW4, HW5 |

Tu 20 Sept | More on semantics of first-order logic (pp. 11–13) | §§16.4–16.7 | HW6, HW7 |

Th 22 Sept | Tableaux for first-order logic (pp. 13–16) | §§21.1–21.6 | HW8 |

Tu 27 Sept | Axiomatic deductions (pp. 16–20) | §§22.1–22.6 | HW9, HW10 |

Th 29 Sept | Deduction theorem and corollaries (pp. 20–23) HW 1–8 due |
§§22.7–22.11 | HW11 |

Tu 4 Oct | Soundness and consistency (pp. 23–27) | §22.12; §§34.1–34.2 | HW12 |

Th 6 Oct | Lemmas for completeness (pp. 27–30) | §§23.1–23.6 | HW13 |

Tu 11 Oct | Completeness, compactness (pp. 30–32) | §§23.8–23.11 | HW14 |

Th 13 Oct | Identity logic (pp. 32–35) | §22.13; §23.7 | HW15, HW16 |

Tu 18 Oct | Unit 1 review and questions | HW17 | |

Th 20 Oct | Theories; Peano and Robinson arithmetics (pp. 36–39)HW 9–17 due. |
§§17.1–17.3; §§33.1–33.4 | HW18, HW19 |

Tu 25 Oct | Naïve foundations (pp. 40–41) | §1.6 | HW20 |

Th 27 Oct | Numerals; Q vs. PA (pp. 41–46) |
§35.1; §35.5 | HW21 |

Tu 1 Nov | Recursive functions (pp. 46–50) | §§29.1–29.7 | HW22, HW23 |

Th 3 Nov | More on recursive functions (pp. 50–53) | §§29.8–29.13 | HW24, HW25 |

Tu 8 Nov | Representing functions in Q (pp. 53–57) |
§35.6–35.9 | HW26, HW27 |

Th 10 Nov | Representing recursion (pp. 57–60) | §§35.3–35.4 | HW28 |

Tu 15 Nov | Arithmetization of syntax (pp. 60–65) | §§34.3–34.5; §34.8; §35.2 | HW29, HW30 |

Th 17 Nov | Fixed point theorem; Gödel’s first theorem (pp. 65–70)HW 18–28 due. |
§§37.1–37.3 | HW31, HW32 |

Tu 22 Nov | No class. Friday class schedule. |
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Th 24 Nov | No class. Thanksgiving break. |
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Tu 29 Nov | Gödel-Rosser and Gödel’s second theorem (pp. 71–73) | §§37.4–37.7 | HW33 |

Th 1 Dec | Löb’s theorem; Tarski’s theorem (pp. 73–75) | §§37.8–37.9 | HW34 |

Tu 6 Dec | Recursive undecidability (pp. 75–78) | §35.10; §36.4; §36.9 | HW35 |

Th 8 Dec | Unit 2 review and questions | HW36 | |

Tu 20 Dec | End of finals week.HW 29–36 due. |