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

## Homework Assigments

Assignments are always due the following class day.

Week of January 4 - January 6, 2007
 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
 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
 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
 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
 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
 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
 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