1. The problem statement, all variables and given/known data What subsets of the real line R are definable in (R;<)? What subsets of the plan R x R are definable in (R:<)? 3. The attempt at a solution R and the empty set are the only definable subsets of (R;<) since: x to x+1 Is an automorphism and changes all subsets except for R and the empty set, therefore those subsets are the only possible definable subsets. R(x) := All x ~(x<x) ie: All real numbers hold this property Empty Set (x) := All x (x<x) ie: Nothing holds this property. Question: When answering the second part of this question for RxR. I'm not completley sure how you can say (a,b) < (c,d). My answer which I'm a little unsure of right now is that you can define (R,a) and (R,a) for some fixed a. (As well as the empty set). Any help would be appreciated.