Home  Homework  Readings 
Week 1  

Day  Topics  Sections 
Monday Jan 4th  Overview: context and motivations (some metamathematics) Notes on notation 
§ 1.1 , 1.2 
Wednesday Jan 6th  Set Arithmetic: unions, intersections, differences, products (finite and indexed)  § 1.4 and pg. 27 
Friday Jan 8th  Paradoxes: Richard's, Russell's, BuraliForti: linear orders and ordinals overview First Order Logic: wellformed statements, arity, language symbols, theories, models 
See Hodges § 1.1 , 1.3 for a simultaneously whimsical and formal treatment of elementary notions in model theory 
Week 2  

Day  Topics  Sections 
Monday Jan 11th  First Order Logic/Model Theory continued: linear orders, groups, fields etc. and a survey of rudimentary results  
Wednesday Jan 13th  The axioms of ZFC "What sort of aggregate is verifiably a set?" Existence of basic set arithmetic in ZFC Justifying defined notation 
§ 1.3, pg. 41, 112, 139 Suppes pg.1418 
Friday Jan 15th  Relations on Sets: binary relations, orderings, functions, higher arity relations etc.  Ch. 2 Hrbacek and Jech 
Week 3  

Day  Topics  Sections 
Monday Jan 18th  No class MLK Jr. Day 

Wednesday Jan 20th  Equinumerosity (Cardinality): Injection, surjection, bijection Finite vs. Infinite Diagonalizing 
§ 4.1 , 4.2 , 4.3 , 3.1 
Thursday (Xhour) Jan 21st  Equinumerosity continued: CantorBernstein (The Onion Theorem) Faithfully representing arithmetic: natural numbers as finite "ordinals" 
§ 3.2 
Friday Jan 22nd  The Omega Recursion Theorem ("Finite" Recursion)  § 3.3 , 4.4 , 4.6 
Week 4  

Day  Topics  Sections 
Monday Jan 25th  Peano Arithmetic The Ordinals! 
§ 3.4 , 6.1 , 6.2 
Wednesday Jan 27th  The Transfinite Recursion (meta)Theorem Ordinals can be as large as you want 
§ 6.3 , 6.4 
Friday Jan 29th  Ordinal Arithmetic  § 6.5 
Week 5  

Day  Topics  Sections 
Monday Feb 1st  Cantor Normal Form  § 6.6 
Wednesday Feb 3rd  The Cardinals! von Neumann cardinal assignment The Hartog (successor cardinal) Aleph hierarchy vs. Beth hierarchy (CH and GCH) 

Friday Feb 5th  Cardinal Arithmetic: For infinite cardinals, addition and multiplication is trivial (The Gödel Ordering) 
Week 6  

Day  Topics  Sections 
Monday Feb 8th  Generalized cardinal sums and products König's Theorem 

Wednesday Feb 10th  Cofinality  
Friday Feb 12th  Cardinal exponentiation part 1 
Week 7  

Day  Topics  Sections 
Monday Feb 15th  Cardinal exponentiation part 2: Characterization using GCH 

Wednesday Feb 17th  Club and Stationary sets: Intersecting less than cofinally many clubs 

Friday Feb 19th  Club and Stationary sets: The diagonal intersection (Fodor's) "Pressing Down" Lemma 
Week 8  

Day  Topics  Sections 
Monday Feb 22nd  Partial ordered sets: Chains, incomparable/incompatible elements Maximal/minimal, greatest/least Zorn's Lemma Filters, subset lattice, ultrafilters 

Wednesday Feb 24th  The club filter and the nonstationary ideal for regular, uncountable κ Dense sets in a poset, a brief glance at Martin's Axiom Solutions to selected exam questions 

Friday Feb 26th  The wellfounded universe Relations on classes and an even more general recursion theorem Transitive models, relations that behave like ∈, and the Mostowski collapse function 
Week 9  

Day  Topics  Sections 
Monday Feb 29th  Absoluteness, relativization Reflection Theorem Downward LöwenheimSkolem The countable transitive model M 

Wednesday March 2nd  The generic filter Names The generic extension M[G] and its minimality The forcing language 

Friday March 4th  nonabsoluteness of cardinality The role of the c.c.c. condition in forcing Forcing over Fn(κ x ω, 2) and the consistency of ZFC + ¬CH 
Week 10  

Day  Topics  Sections 
Monday March 7th  Presentations  
Final Exam Assigned March 8th15th 
The final exam will be administered and due within this time frame. Details TBA. 