Martin Flashman's Courses -

Math 499 Independent Study for Natalya Jackson
Logic and Set Theory

Assignments (tentative)

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Last updated: 8/20/2012

TEXTS: What Is Mathematical Logic? by J.N. Crossley et al. (Oxford,1972)
Logic for Mathematicians by A.G. Hamilton (Cambridge,1978+)
Set Theory and related topics by S. Lipshutz ( Schaum/ Mcgraw Hill,?)

Assignments - (subject to change) 8-20-2012 
Week Monday
Other?
 Reading Problems 
Due on Thursday 
of the next week
1 Informal 
Statement 
Calculus		 Introduction:1.1,1.2 
Statements, Connectives, 
and Truth Functions
Products of sets, 
Truth Tables		 C:1-History-(4 weeks) 
H: 1.1,1.2 
L: 4,5,14		 H. ch.1: 1,2,3(a-e,h),5(a,c),6a,7 
L: ch 5: 7,25,26,32 
    ch 14: 26, 28, 34, 37, 38
2  1.3 
Statement Forms 
and Substitution
1.5  Connectives 
Arguments Preview		 H: 1.3-1.5 H. ch.1: 8, 9, 11a, 14a, 15a, 16, 17
3 
Formal 
Statement 
Calculus		  1.6, 2.1 
Arguments 
Begin Formal Logic (L)
2.1 Proofs 		 H: 1.6,2.1 H. ch.1:20, 21 
ch.2: 1(a,b), 2(a,b), 3(a,b)
4    2.1 The Deduction Theorem
2.2 Valuations-Completeness of L (Adequacy)		 H: 2.2 H. ch. 2: 6-8,10,11
5 
Informal 
Predicate 
Calculus		  Completeness continued 
Complete and consistent extensions-
Adequacy finished! 


6 3.1 Begin Predicates and quantifiers.
3.2 First Order Languages. 
H: 3.1,3.2 
L: 6,15		 H. ch. 3: 1,2, 6, 7, 9(a,b)
7 
Formal 
Predicate 
Calculus		 3.3 Interpretations 3.4 Valuations 
H: 3.3, 3.4 
L: 17 
C: 2 (2 weeks)		 H. ch. 3: 11, 12, 14(a-c), 15(a-c),16
8  3.4 Truth and Validity 
H: 4.1
9 
 Finish Truth and validity 
4.1 Begin KL.Axioms,Rules,Proofs
Soundness 
The Deduction Theorem 
Preparing for Adequacy		 H:4.1,4.2 H:4.1: 1 - 3
10 The Adequacy Theorem
Adequacy.		 H:4.4
C: ch 2		 H: 4.4: 12-14
11 More on Adequacy
Finish Adequacy
Begin  Models
H:4.5, 5.1,5.2
C:ch 3		 H: 4.5:16-18,20
12 Equality 
Equivalence relations
1st Order Arithmetic
Formal Set Theory- 		 H:5.4, 5.5
C:ch  6
SOS: 6,7,9		 H:5.2: 2,5,6
SOS: Ch.7:12-14,28
13 Axiom of Choice and The Continuum Hypothesis
Begin work on formal arithmetic
Recursive functions and relations		 H: 6.1,6.2,6.3
C: ch 4
14 Godel's Incompleteness Theorem
Breath		 C: ch 5
15


16


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