**Course.**

Math 116b Winter 2018

1:00-2:25 TR, B127 GCL

**Instructor.**

Aristotelis Panagiotopoulos

Building 15, office 210-5
*panagio at caltech.edu*
**Office hours.**
Mondays 4-5 PM, Office 210-5, Building 15

**Books.** This class will be based on a complilation of book chapters and notes. It will therefore be important for each of you to have access to class notes.That being said, Enderton's "Elements of set theory" is going to be relevant for large parts of the quarter. For a more advanced book one may look at Kunen's "Set theory". Finally, a pleasant read for the last weeks of the quarter (or afterwards) might be Weaver's "Forcing for mathematicians".

**Homework.**

HW1. (Solutions),

HW2.

**Calendar.**

- (Jan 23) Pigeonhole principle; trees; Konig's lemma; Infinite Ramsey theorem.
- (Jan 18) Axiom of choice and various notions of infinity; Countable sets, aleph-zero and properties; Cantor's powerset theorem.
- (Jan 16) Ordering on ω; Integers, Rationals, Reals; Infinite vs Dedekind infinite.
- (Jan 11) Construction of (ω,0,s,+,*); transitive sets; definition by recursion II.
- (Jan 9) Products, functions and other constructions from the axioms; number systems; definition by recursion.
- (Jan 4) Russel's Paradox; Zermelo's axioms and universe.

**Home.**
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