Martin Flashman's Courses - Math 446 Spring, '02

MATH 446 Logic and Set Theory Assignments


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Last updated: 4/08/02

TEXTS: What Is Mathematical Logic? by J.N. Crossley et al. (Oxford,1972)
Logic for Mathematicians by A.G. Hamilton (Cambridge,1978+)

Assignments - (subject to change) 4-8-02
Week Monday Wednesday Friday Reading Problems 
Due on Wednesday  
of the next week
1 Informal 
Statement 
Calculus
1-21 MLK Day 1-23 Introduction:1.1,1.2 
Statements, Connectives, 
and Truth Functions
1- 25 
Truth Tables
C:1-History-(4 weeks) 
H: 1.1,1.2 
Due :1-30: 
H. ch.1: 1,2,3(a-e,h),5(a,c),6a,7 
2 1-28 1.3 
Statement Forms 
and Substitution
1-30 2-1 1.5 
Connectives 
Arguments Preview
H: 1.3-1.5 Due: 2-6: 
H. ch.1: 8, 9, 11a, 14a, 15a, 16, 17
3 Formal 
Statement 
Calculus
2-4 Products of sets 2-6  1.6, Arguments  2-8 2.1 Begin Formal Logic (L) 
Proofs 
H: 1.6, 2.1 Due 2-13: 
H. ch.1:20, 21 
ch.2: 1(a,b), 2(a,b), 3(a,b)
4 2-11  2.1 More on proofs and The Deduction Theorem 2-13 Deduction applications. 
Begin valuations.
2-15 2.2 Valuations-Soundness and Completeness of L (Adequacy) H: 2.2 Due 2-20 Extended to 2-27! 
H. ch. 2: 6-8,10,11

Informal 
Predicate 
Calculus
2-18 Completeness continued  2-20 Extensions: Complete and consistent 
...a proof of adequacy.
2-22 Complete and consistent extensions- Adequacy finished! Begin Predicates and Quantifiers? H: 2.2 cont'd. 
H: 3.1 
Due 2-27 (Extended from 2-20.) 
H. ch. 2: 6-8,10,11 
H. ch. 3: 1,2
6 2-25 3.1 Begin Predicates and quantifiers. 2-27More on Predicates... valuations 3-1 3.2 First Order Languages. 
3.3 Interpretations 
3.4 Valuations ,Truth and Validity 
H: 3.1,3.2  Due : 3-6 
H. ch. 3: 6, 7, 9(a,b)

Formal 
Predicate 
Calculus
3-4 3.4 Truth and Validity  3-6 Truth and validity  3-8  Finish Truth and validity  H: 3.3, 3.4 
C: 2 (2 weeks)
Due 3-13 
H. ch. 3: 11, 12, 14(a-c), 15(a-c),16
8 3-11 Finish Truth and validity. 3-13 
4.1 Begin KL
Axioms,Rules,Proofs Soundness
3-15More on Proofs: The Deduction Theorem. 
Preparing for Adequacy
H: 4.1 Due: 3-27 
H:4.1: 1 - 3

Spring Break
3-18 No Class 3-20 No Class 3-22 No Class
10 3-25 The Adequacy Theorem. 3-27More on Adequacy 3-29 Adequacy H:4.1,4.2, 4.4 
C: ch 2
Due: 4-5 (Friday) 
H: 4.4: 12-14
11 4-1 NO Class! 
CC Day
4-3 finish Adequacy. 
Begin  Models 
4-5 Begin Equality and 
Equivalence relations 
H:4.4.4.5, 5.1,5.2 
C:ch 3
Due: 4-17 !!! 
H: 4.5:16-18,20
12 4-8 More Equality and Equivalence relations and Normal models. 4-10  1st Order Arithmetic 4-12 Reading Day- NO class 
Watch Video: A Non-Euclidean Universe.
H:5.1, 5.2,5.4,5.5. DUE:4-17. Brief report/paper on Video- How does Consistency prove Independence with models?
13 4-15 1st Order Arithmetic 4-171st Order Arithmetic  4-19 Begin work on Formal Set Theory H:5.4, 5.5 
C:ch  6 
Handout:SOS: 6,7,9 
Due Monday: 4-29 
H:5.2: 2,5,6 
SOS: Ch.7:12-14,28
14 4-22 4-24 Axiom of Choice and The  Continuum Hypothesis 4-26  Formal arithmetic: Godel's Incompleteness Theorem (Introduction)  H: 5.5, 6.1,6.2,6.3 
C: ch 4
15 4-29 Godel's Incompleteness Theorem. 
Recursive functions and relations (Introduction)
5-1Breath 
More on Set Theory.
5-3 Final exam distributed.More Set Theory. Zorn's Lemma C: ch 5
16 5-6 Cantor Bernstein. Start Turing Machines 5-8 More Turing Machines 5-10 A final look at the Continuum Hypothesis
17 5-13 Final Exam Period 5-15 Final Exam Period 5-17 Final Examination  
DUE by 5 pm!
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