Math 39 Homework #13

It requires a very unusual mind to make an analysis of the obvious.
Alfred North Whitehead

Quiz

There will NOT be a quiz on Monday in honor of your exam on Tuesday 10/27.

Reading

Read what we will cover in the next class: 3.4, 4.1, 4.2.

When reading 3.4 pay special attention to the following concepts:

  • the proof of Propositions 3.23.
When reading 4.1 pay special attention to the following concepts:
  • the Deduction Theorem and the use of the Deduction Theorem in the examples following its proof.
When reading 4.2 pay special attention to the following concepts:
  • provably equivalent.

Problems

The following problems are due by the beginning of class on Monday 10/26.
  • 4.1: 1, 3.
  • Prove that if an L-wf A is contradictory, then A is not a theorem of K(L).
  • Prove that if A(x1) is an L-wf and c is a constant, then {A(x1)} deduces A(c).
  • Let P be a one-place predicate and
    let Gamma1 = { ~(\forall x1) P(x1), P(x1), P(x2), P(x3),...} and
    let Gamma2 = { (\forall x1) P(x1), ~P(x1), ~P(x2), ~P(x3),...}.
    Is either of Gamma1 or Gamma2 consistent?