## MATH 446 Logic and Set Theory Assignments

Last updated: 2/26/98

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) 3-24-98
Due on Thursday
of the next week
1 Informal
Statement
Calculus
1/20
Introduction:1.1,1.2
Statements, Connectives,
and Truth Functions
1/22
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 1/27 1.3
Statement Forms
and Substitution
1/29 1.5
Connectives
Arguments Preview
H: 1.3-1.5 H. ch.1: 8, 9, 11a, 14a, 15a, 16, 17

Formal
Statement
Calculus
2/3 1.6, 2.1
Arguments
Begin Formal Logic (L)
2/5 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 2/10
2.1 The Deduction Theorem
2/12 2.2 Valuations-Completeness of L (Adequacy) H: 2.2 H. ch. 2: 6-8,10,11

Informal
Predicate
Calculus
2/17 Completeness continued

2/19 Complete and consistent extensions- Adequacy finished!

6 2/24
3.1 Begin Predicates and quantifiers.
2/26
3.2 First Order Languages.

H: 3.1,3.2
L: 6,15
H. ch. 3: 1,2, 6, 7, 9(a,b)

Formal
Predicate
Calculus
3/3 3.3 Interpretations  3/5 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 3/10 3.4 Truth and Validity  3/12 3.4 Truth and Validity  H: 4.1

Spring Break
3/17 No Class 3/19 No Class
10 3/24 Finish Truth and validity
4.1 Begin KL.Axioms,Rules,Proofs
3/26 Soundness
The Deduction Theorem
H:4.1,4.2 H:4.1: 1 - 3
C: ch 2
H: 4.4: 12-14
Begin  Models
H:4.5, 5.1,5.2
C:ch 3
H: 4.5:16-18,20
13 4/14 Equality
Equivalence relations
4/16 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
14 4/21 Axiom of Choice and The Continuum Hypothesis
Begin work on formal arithmetic
4/23 Recursive functions and relations H: 6.1,6.2,6.3
C: ch 4
15 4/28Godel's Incompleteness Theorem 4/30 Breath C: ch 5
16 5/5 5/7