Introduction to set theory
Mathematics M114S and Philosophy M134,
L 26, 27, 28, Last week of the term. Will cover the basic
properties of ordinal numbers in Chapter 12 and review the class.
(Working on the suggested Problems and Exercises in Homework will help understand these lectures.)
L25, 3/9, F. Will complete the discussion of some of the
remaining material in Chapter 11, primarily 11.18, 11.26 - 11.31
and 11.34 - 11.36, and then start on Chapter 12, which we will
cover (almost) completely.
Look in the Homework page for some suggested problems from
L24, 3/7, W. Continued in Chapter 11, which we will not
cover completely. Combined with the parts we covered on Monday,
we have completed 11.1 - 11.14 and discussed some further
L23, 3/5, M. Introduced the Axiom of Replacement in
Chapter 11 and derived some of its elementary consequences.
L22, 3/2, F. Will review Chapters 7, 8 and 9 on which the
second midterm will be based.
L21, 2/28, W. Will finish Chapter 9---mostly giving the
(not simple) proof of König's Theorem 9.21.
L20, 2/26, M. Continued in Chapter 5, through
(almost) the proof of 9.16.
L19, 2/23, F. Continued in Chapter 9, not following
exactly the order in the book.
L18, 2/21, W. Will finish Chapter 8 on the basic facts
about AC and start on Chapter 9, aiming to get to 9.7.
L17, 2/16, F. Will review Chapter 7, prove the Fixed Point
Thm. 7.35 and start on Chapter 8.
L16, 2/14, W. Will cover most of the remaining material in
Chapter 7, most significantly Hartogs' Thm 7.34.
L15, 2/12, M. Will start with the Iteration Lemma 7.25 and
get (at least) through the comparability of well ordered sets and
its corollaries, 7.32 and 7.33.
L14, 2/9, F. Will continue with the theory of
welloredrings, starting with 7.7 and aiming to get through the
Iteration Lemma 7.25.
L13, 2/7, W. Will go over 6.1 - 6.18, the parts of Chapter
6 that we will cover, and then start on Chapter 7 which we will
cover in full.
L12, 2/5, M. Will review the parts of Chapters 1 - 5 that
we have covered (and on which the test will be based).
L11, 2/2, F. Will continue with Chapter 5 and finish the
part of it that we will cover.
L10, 1/31, W. Will review and continue with Chapter 5,
aiming to get through at least 5.15 (properties of addition).
L9, 1/29, M. Started on the natural numbers in Chapter 5,
stopped somewhere in the middle of the proof of 5.7.
L8, 1/26, F. Did not get as far on W, so the goal is the
same: will finish Chapter 4 and start on Chapter 5, aiming to get
L7, 1/24, W. Will finish Chapter 4 and start on Chapter 5,
aiming to get to 5.6.
L6, 1/22, M. Will start on Chapter 4, aiming to get (at
least) to 4.14.
L5, 1/19, F. Went through Chapter 3, a bit quickly,
skipping much of the discussion; make sure you read the Chapter
if you want to get a good understanding of this material.
L4, 1/17, W. Review Chapter 2 briefly and start on Chapter
3, try to get through 3.17. There is a lot of "talk" in this
Chapter and I will cover it lightly: it will really help your
understanding of this lecture if you read ahead of time pages 19
L3, 1/12, F. Will aim to finish Chapter 2. Got through
2.18. The remainder of the Chapter will be covered by Assaf in
the Section meeting on Tuesday, Jan. 16.
L2, 1/10, W. Chapter 2, through Cor 2.14, the
uncountability of the real numbers. (I will skip many details, so
it will really help if you read through this material before
L1, 1/8, M. Will review briefly the material in Chapter 1
and start with Chapter 2, aiming to reach 2.7.