Logic Problems

No, not like fun logic puzzles, but problems for mathematical logic.

For Friday, 1 September, write the argument presented in your proofs class to prove that the real numbers are uncountable.

For Monday, 11 September, write up detailed solutions to the following five problems: 1.5.6, 1.6.7, 1.7.2, 1.8.2, and 1.9.4.

For Monday, 25 September, write up detailed solutions to the following three problems: 2.2.4, 2.4.6, 2.5.1

For Friday, 6 October, write up detailed solutions to 3.2.2-5. This may be submitted as a group.

For Monday, 23 October:

1. Complete the alternate model construction for Q that is begun on the bottom of page 69, and left open on the top of page 70.

2/3. Complete two more of the order-adequate proofs that are left remaining in section 11.8.

4/5. Complete two of the listed results in Theorem 12.1, not including 1,2,4,7.

6. Prove that the Fibonacci function (F(0)=1, F(1)=1, F(n) = F(n-1) + F(n-2)) is primitive recursive. Be as precise as possible in your justification.

Here's the optional last problem set, due Monday, 4 December.

1. Compare and contrast
Theorem 21.1
Theorem 24.2
and the formalised first theorem (F on p. 235).

2. Prove, as indicated on the bottom of p. 250, if T is omega-consistent, then T cannot prove the negation of G'.

3. Answer the question in footnote 3 on p. 251.

4. Pick one of the exercises in §3.3 of Chris' book. Complete it.