Math 29 Homework #25

The following quote was hanging outside a restaurant:
Good food is not cheap
Cheap food is not good
Do these two sentences say the same thing or different things? Raymond Smullyan

Reading

Read what we covered in today's class: 7.3
Read what we will cover in the next class: 7.4, 9.4

When reading 7.3 pay special attention to the following concepts:

  • definition of productive sets, why are we interested in these sets?, also, pay special attention to Theorems 3.2, 3.4 (these provide us with lots of examples of productive sets), definition and examples of creative sets, Theorem 3.11 is also very important.
When reading 7.4 pay special attention to the following concepts:
  • the definition of simple sets, Theorem 4.2 which notes that simple sets are noncomputable and not c.e., and Theorem 4.3 which establishes the existence of simple sets
When reading 9.4 pay special attention to the following concepts:
  • URMO, URMO-computability, Theorem 4.3, note the many later results which come from lifting known URM-results to URMOs

Problems

The following problems are due by the beginning of class on Friday 5/21.
  • p. 139, # 7.3.13.4
  • p. 139, # 7.3.13.6a
  • p. 132, # 7.2.18.7 (previous section!)
  • p. 139, # 7.3.13.9

Presentations

  • Joran, Theorem 7.2.16 on Monday 5/17
  • David, Theorem 7.3.2 and 7.3.4 on Wednesday 5/19
  • Amanda, Theorem 7.4.2 and 7.4.3 on Wednesday 5/26