09ma6cHW7

09ma6cHW7 - Ma/CS 6c Assignment #7 Due Thursday, May 27 at...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 first-order definable in the structure N = h N ; 0 ,S, + i . (It turns out that these are the only first-order 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 first-order 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 first-order definable subsets (i.e., unary relations) of M = Z Z . (20%) 4. Consider the language L = { < } and it structure A = h R ,< i ....
View Full Document

Page1 / 2

09ma6cHW7 - Ma/CS 6c Assignment #7 Due Thursday, May 27 at...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online