MATH 385 Midterm: MATH 385 Amherst F08M34Dans

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 385
• Professor: All

Document Summary

Rules: you may use your notes and your textbook, but no other books. Due friday, dec. 19, at noon: (10 points) in this problem p is a 1-place predicate symbol and c is a constant sym- bol. Find a deduction of xp x from { x( p x p c), p c}. This is now problem 1 in proof check. You should specify the language you are using and the formulas and , and you should give a proof that x( ) ( x ) . (of course, in your example, x will occur free in . This shows that the hypothesis that x does not occur free in was necessary in part (a). ) (c) show that ( x ) ! X( ). (notice that there is no assumption in this part about whether or not x occurs free in . : (10 points) suppose t1 and t2 are theories (in the same language).