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Unformatted text preview: Ma/CS 6c Assignment #7 Due Thursday, May 27 at 1 p.m. (20%) 1. Call a set X N eventually periodic if there is n N and p N ,p 1 (a period ) such that for all n n , n X iff n + p X. Show that every eventually periodic set is firstorder definable in the structure N = h N ; 0 ,S, + i . (It turns out that these are the only firstorder definable sets in N .) We of course identify here subsets of N with unary relations on N . The language here is L = { 0; S, + } . (20%) 2. Show that + is not firstorder definable in the structure N 00 = h N , i . The language here is L = {} . (20%) 3. * Consider the language L = { f,g } with f,g unary function symbols, and its structure M = h Z Z ,f M ,g M i , where f M ( i,j ) = ( i,j + 1) g M ( i,j ) = ( i + 1 ,j ) . Determine all the firstorder definable subsets (i.e., unary relations) of M = Z Z . (20%) 4. Consider the language L = { < } and it structure A = h R ,< i ....
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 Spring '09
 InessaEpstein
 Math

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