Math 69
Logic
Last updated June 25, 2009 14:49:00 EDT

General Information Syllabus HW Assignments

Homework Assigments

Assignments are always due the following class day.

Week of January 4 - January 6, 2007
Assignments Made on:
Friday:
  • Read: Chapter 0
  • Write up: Undergrads: Ex. 3 p. 19. Grads: prove unique interpretation of a wff.
Saturday:
  • Read: 1.2 including exercises.
  • Write up: Ex. 1 p. 27; and find a wff on {A,B,C,D} which is true iff exactly half the sentence symbols are true.
Week of January 8 - January 12, 2007
Assignments Made on:
Monday:
  • Read: 1.5,1.6
  • Write up: Ex. 2 p. 59.
Wednesday:
  • Read: 1.7
  • Write up: Find an inconsistent set of wffs any three of which are consistent.
Friday:
  • Reread: 1.7
  • Write up: Ex. 11 p. 66
Week of January 16 - January 19, 2007
Assignments Made on:
Tuesday:
  • Read: 2.1
  • Write up: Ex. 1 and 2, p. 79
Wednesday:
  • Read: 2.2 (except for Homomorphisms section)
  • Write up: Write as wffs (not super-formally) the following sentences in the language of graphs: (a) G contains three vertices any two of which are adjacent; (b) G contains three vertices no two of which are adjacent; (c) G has more than 5 vertices; and (d) if (c) holds than (a) or (b) must hold.
Friday:
  • Read:
  • Write up: Ex. 2 p. 99 and Ex. 9 p. 100
Week of January 22 - January 26, 2007
Assignments Made on:
Monday:
  • Write up: (1) Draw pictures of all non-isomorphic graphs on 4 vertices; (2) Find a theory of graphs which has models of all even sizes but none of any odd size.
Wednesday:
  • Write up: (1) Find out what a group is, and compose a set of axioms for groups in a language with constant "1" (for the identity), a binary operation (multiplication) and a unary operation (inverse). (2) Do the same with just "1" and a binary operation intended to stand for "x times (y inverse)".
Friday:
  • Write up: A lattice is a poset in which every two elements have a least upper bound and a greatest lower bound. (1) Give axioms for the theory of lattices, in the language of posets (just a binary relation for "less than"). (2) Can you define the "less than" relation in a lattice which comes only with binary operations for lub and glb?
Week of January 29 - February 2, 2007
Assignments Made on:
Monday:
  • Read: 2.4
  • Write up: Ex. 2 p. 129
Wednesday:
  • Prepare for midterm exam
Friday:
  • Mid-term exam (in class)
Week of February 5 - February 7, 2007
Assignments Made on:
Monday:
  • Read: Deductions and Metatheorems, beginning p. 116
Tuesday:
  • Write up: Ex. 4 and 6, p. 130
Wednesday:
  • Write up: Ex. 3 and 4, p. 99(!)
Week of February 12 - February 16, 2007
Assignments Made on:
Monday:
  • Write up: p. 145, Ex 2 and 3 ("soft")
Wednesday:
  • Snow day
Friday:
  • Write up: Prove that if a set of wffs has arbitrarily large finite models, then it has an infinite model.
Week of February 19 - February 23, 2007
Assignments Made on:
Monday:
  • Write up: (1) Write precisely the statement of Ramsey's Theorem which begins "for any m, c and k there is an n..."; (2) Prove that in any infinite set with a symmetric anti-reflexive ternary relation P, there is an infinite subset all of whose triples are in P, or an infinite subset none of whose triples are in P.
Wednesday:
  • Write up: Problems 2 & 3, pp. 162-3
Friday:
  • Write up: Problem 6, p. 193
Week of February 26 - March 2, 2007
Assignments Made on:
Monday:
  • Write up: Problem 1, p. 223
Wednesday:
  • Read: pp. 210-223
  • Write up: The rest of the proof (product and exponentiation cases) of Lemma 33B, p. 204.
Friday:
  • Review: Sequence numbers and recursion
Week of March 5 - March 7, 2007
Assignments Made on:
Monday:
  • Prepare: (by yourself) for question on final about theory of dense linear orderings without endpoints plus new axioms c_1 < c_2, c_2 < c_3, ...
Wednesday:
  • Prepare for Final Exam , 8:00 am Saturday, March 10, venue to be announced.


Pete Winkler
Last updated June 25, 2009 14:49:00 EDT