MATH 385 Final: MATH 385 Amherst F10M34Final
15 Feb 2019
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Rules: you may use your notes and your textbook, but no other books. Due wed. , dec. 22 at 5:00 pm: (12 points) suppose and are sets of sentences in some rst-order language. = { | and }. B mod(t ) and a is a substructure of b then a b. (recall that this means that for every formula and every function s : v |a|, (cid:15)a [s] i (cid:15)b [s]. Hint: prove this by induction on formulas. : (12 points) suppose that and are sets of formulas, and and are formulas such that (cid:15) ( ). Prove that there is a formula such that (cid:15) ( ) and. Prove that x y( ) (cid:15) y x( ). (b) give an example of formulas and (in some rst-order language) such that. We will write i to indicate that there is an instantiationless deduction of (from no premises). Now for each formula we de ne h( ) recursively as follows:
