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Tuesday January 4 |
Course overview. Applications of Compactness PDF text: Section IV.11 and V.4., start of II.2. Hodel text: Section 6.1 Screen slides from lecture. Zoom meeting uploaded to canvas. No in-class worksheet. |
Thursday January 6 |
Overspill, Theories, Nonstandard model of the integers, etc. PDF text: Sections IV.11 and V.4. Hodel text: Sections 6.1. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Tuesday January 11 |
Topics TBA. Prepare by reading sections IV.11, V.5 and the proof of Completeness Theorem. PDF text: Sections IV.11, V.3, V.5. Hodel text: Sections 6.2. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Thursday January 13 |
Algorithms (Informal). To prepare, start reading Chapter V. PDF text: Sections VII.1, VII.2, VII.3. Hodel text: Section 1.8. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Tuesday January 18 |
More on computability. Prepare by reading sections VII.1-3. PDF text: Sections VII.3. Hodel text: Section 1.8. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Thursday January 20 |
Algorithms for propostional and first-order logic. PDF text: Section VII.4 and VII.5. Hodel text: N/A. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Tuesday January 25 |
Regular expressions, Axiomatiability and decidability, Cantor's theorem, Undecidability results. PDF text: Section VII.7. Hodel text: N/A. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Thursday January 27 |
Halting problems and Undecidability PDF text: Section VII.4 and VII.5. Hodel text: N/A. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Tuesday February 1 |
Introduction to Turing machines. PDF text: Section VIII.1. Hodel text: N/A. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Thursday February 3 |
More on Turing machines PDF text: Section VIII.1 and VIII.2. Hodel text: N/A. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Thursday February 10 |
Church-Turing thesis, Malleability, Universal Turing machine PDF text: Section VIII.3 and VIII.4 (to be written). Hodel text: N/A. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Tuesday February 15 |
Self-referential algorithms. Rice's Theorem. PDF text: Section VII.6.3-VII.6.5 and VII.7. Hodel text: Section 9.5. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Thursday February 17 |
Computable inseparability, Theories of arithmetic Q, PA, R. Representability. PDF text: Sections VII.6, IX1, IX.2. Hodel text: Section 7.1. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Tuesday February 22 |
Theories of arithmetic Q, PA, R. Representability. PDF text: Section IX.2, IX.3. Hodel text: Section 7.1, 7.2, 7.3, 7.4. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. |
Thursday February 24 |
Proofs of the First Incompleteness Theorem. PDF text: Section IX.4. Hodel text: Section 7.1, 7.2, 7.3, 7.4, 8.6. Screen slides from lecture. In-class worksheet Zoom meeting uploaded to canvas. Classroom meeting on podcast and Canvas. |
Thursday February 24 |
First Incompleteness Theorem. PDF text: Section IX.4.1-IX.4.3. Hodel text: 7.4, 7.5. No PDF slides (Chalk talk) or in-class worksheet today. Zoom meeting uploaded to canvas (first 20 minutes missing). Recording available on podcast.ucsd.edu |
Tuesday March 8 |
Second Incompleteness Theorem. PDF text: Chapter IX.8. Hodel text: 7.4. Screen slides from lecture. Zoom meeting and podcast recording uploaded to canvas. Recording available on podcast.ucsd.edu |
Thursday March 10 |
Representability. PDF text: Chapter IX.6-IX.8. Hodel text: 7.3. Screen slides from lecture. Zoom meeting and podcast recording uploaded to canvas. Recording available on podcast.ucsd.edu |