Math 39 Homework #9 The whole of science is nothing more than the refinement of everyday thinking. Albert Einstein

	Reading Read what we will cover in the next class: 3.4 & 3.5. When reading 3.4 pay special attention to the following concepts: valuation, i-equivalent valuations, satisfaction, Proposition 3.23, true vs false wf, Propositions 3.26 - 3.29, tautology & Proposition 3.31, closed wf, closed wfs and interpretations logically valid wf, contradictory wf. When reading 3.5 pay special attention to the following concepts: Skolem function, skolemized form of wf, Proposition 3.39.

	Problems The following problems are due by the beginning of class on Friday 10/16. 3.2: 9. 3.3: 11, 12, 13 (you might want to do the following first). Let L = { a1, A11, A21, f21 } = { c, P1, P2, f }. Give two different examples of L-interpretations. One of these should have both P1, P2 finite and the other have both P1, P2 infinite. Let L = {c, f11,f21} and M={N, 0, S, +} be an L-interepretation where N is the natural numbers and each of the specified parameters has its standard meaning in N. Define a valuation V on M by V(x0) = 0, V(x1) = 2, V(x2) = 4 and V(xi) = 0 for i > 2. Define a valuation W on M by W(x0) = 3, W(x1) = 2, W(x2) = 1 and W(xi) = 0 for i > 2. Determine V(t) and W(t) for each of the following terms: x0 x1 0 S(x1) S(x2) x0 + x2 + 0