L28, 6/4, F, Plan. Will finish reviewing for the final exam.
Fact. Did that, that's all folks!
L27, 6/2, W, Plan. Will give the Second Proof of Gödel's First Incompleteness Theorem
and start reviewing for the final exam.
Fact. Did that.
L26, 5/28, F, Plan. Will prove Tarski's Theorem and go on to state Gödel's First Incompleteness
Theorem and cover (at least) the first of the two proofs of it we will give.
Fact. Did that.
L25, 5/26, W, Plan. Aim to finish Section 1 and (perhaps) Lemma 2.1 of the Notes for Part 3.
Fact. Finished Lemma 2.1, moved on to cover Lemma 2.2 and Def. 2.3, and also stated
(on the last slide) Theorem 2.4, Tarski's Theorem, without proving it.
L24, 5/24, M, Plan. Will start on Part 3, The theorems of Tarski and Gödel.
Fact. Got through 1.4 in the Notes for Part 3 and then started with the parts of Def 1.5 and
the key Lemmas 1.6 and 1.7 that have to do with terms.
L23, 5/21, F, Plan. Will introduce and motivate codings, the key new idea we will
use in Part 3 of the course.
Fact. Did that.
L22, 5/19, W, Plan. Introduce elementary extensions and substructures,
mostly to review for the test.
Fact. Did that.
L21, 5/17, M, Plan. Will discuss non-standard models and finish Part 2 of the Notes.
Fact. Got there.
L20, 5/14, F, Plan. Finish and review Section 7C, then start on Sections 7D and 7E,
aiming to finish Part 2 of the Notes.
Fact. As usually, I did not get to discuss the last slide on non-standard models
L19, 5/12, W, Plan. Aim to finish 7C and the proof of the Completeness Theorem.
Fact. All but got there---did not discuss the last slide in the file of slides.
L18, 5/10, M, Plan. Will cover def 7C.13 of Henkin sets and prove Lemmas 7C.14 and 7C.15.
Fact. Got to but did not finish the proof of Lemma 7C.15.
L17, 5/7, F, Plan. Will start with a brief review of some of the ideas in Lemmas 7C.1 -- 7C.6 and then begin the
proof of the Completeness Theorem 7C.7. Aim to get through Lemma 7C.14.
Fact. Got through the statement and proof of Lemma 7C.11 and also gave an discussed Def. 7C.12. Key parts of this
lecture were the definitions of consistency, strong consistency and completeness for a theory T.
L16, 5/5, W, Plan. Start with the Proof System in 7A, outline the proof of the Soundness Theorem in
7B, aim to get started with the crucial 7C. Try to read ahead.
Fact. Got through 7C.7, albeit a little hurriedly towards the end.
L15, 5/3, M, Plan. Will finish Section 6 and start on the Proof Theory for LPCI in Section 7, aiming to
describe the axioms in Diagram 1 and at least explain the Soundness Theorem 7B.1.
Fact. Got as far as listing the Hilbert Proof System for LPCI, no time to discuss it.
L14, 4/30, F, Plan. Will take 10 minutes or so reviewing the material in Section 5 and
discussing the examples in 5C; and then will cover the (brief) Section 6.
Fact. Ran out of time just before the discussion of Peano Arithmetic in 6B.4.
L13, 4/28, W, Plan. Aim to go through the rest of Section 5, lightly (as explained in Lecture 12),
skipping many proofs.
Fact. Got through 5B, did not discuss the examples in 5C.
L12, 4/26, M, Plan. Will start with a brief review of what we covered in L11; then go on to cover
some material we have skipped in Sections 3B - 3G---this has little mathematics but it has a lot of
definitions, please read ahead; and then will start Section 5, aiming to finish 5A.
Fact. Got through 5A.2.
L11, 4/23, F, Plan. Will start with the proof of the Chinese Remainder Theorem 4A.3 and aim
to finish Section 4.
Fact. Well,I did, but rather hurriedly at the end.
L10, 4/21, W, Plan. Will review 3J and then start on Section 4 and aim
to get (at least) through 4A; there are proofs involved, this is a case where it will
really pay to read ahead.
Fact. Got to stating the Chinese Remainder Theorem 4A.3, but did not get to the proof.
Important Note. At this point, we have postponed for later
Sections 2E, 3B, 3C, 3D and Part (1) of Theorem 3G.1. We will cover this material when we need it.
L9, 4/19, M, Plan. Start with 3B, aim to go through 3I.
Fact. As planned, except that I put off some parts (especially in
3H) for later and rushed through 3J.
L8, 4/16, F, Plan. Aim to cover Sections 2C - 2F of LPCI.
Fact. Skipped 2E and 2F (later); covered 3A and 3E.
L7, 4/12, M, Plan. Start on LPCI, review (very quickly) Section 1 and start on Section 2,
aiming to get to the end of 2B.
Fact. Did just that.
L6, 4/9, F, Plan. Prove Part (2) of the Completeness Theorem and review PL.
Fact. Did just that.
L5, 4/7, W, Plan. Start with some general remarks (and
review), prove the Soundness Theorem 3B.1 and then start with the
rest of 3B aiming to finish it. (The proof of the Completeness
Theorem 3B.5 is the most important part of PL---try to read
through it before before the lecture.)
Fact. Got through the proof of Part (1) of the Completeness Theorem.
L4, 4/5, M, Plan. Aim to cover Section 3A.
Fact. Got to the end of 3A -- barely.
L3, 4/2, F, Plan. Start with 2C.1 (The Tarski conditions) and go to (at least)
the end of Section 2.
Fact. Finished Section 2 and just (barely) started on Section 3.
L2, 3/31, W, Plan. Discuss 1B and then start on Section 2,
aim to finish 2A.
Fact.
Did a bit more: defined assignments and the satisfaction relation on p.
7 of the Notes.
L1, 3/29, M, Plan. Will make some general remarks about the
course and cover Section 1 of PL, pp. 1 - 3.
Fact. Skipped
1B on p. 3 and the last paragraph of Section 1 on the
biconditional; read this.