80-110 The Nature of Mathematical Reasoning

Thursday, July 20 2000

Quiz 5

      Name: _______________________________

  1. What is the arity of a predicate?

  2. A number that tells you how many names it needs to form an atomic sentence. (FOL, p.12)

  3. In Tarski's World, can an object have more than one name? How about in our world?

  4. Yes, the same object can have different names in Tarski's World and also in ours. (FOL, p.10)

  5. In which century were the axioms for arithmetic formulated?

  6. Late 19th century: Dedekind (1888) and Peano (1889). (Lecture 7/19/00)

  7. How can you show that an axiom system is consistent?

  8. By presenting a model for the axiom system, i.e., an interpretation that satisfies all the axioms. (Lectures 7/17-19).

  9. What do (axiomatic) mathematical theories consist of? Which part(s) have we not disussed in class yet?

  10. Definitions, Axioms, Theorems, Inference Rules. We have not discussed Inference Rules yet, but we will in a few days!