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I understand that integers are not definable in the real numbers using addition. My problem is that I don't know where it fails.

   Question: *Are integers definable in the reals using addition? Justify your answer.*

I also understand it should have something to do with an automorphism. I have all the generals without specifics. Can anyone help me out?

Bobby
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    What do you know about: (i) What automorphisms of $(\mathbb{R};+)$ look like? (ii) How automorphisms relate to definable sets? – Noah Schweber Nov 11 '20 at 14:45
  • It depends. If you assume that constants like $0, 1$ are defined (being the neutral elements of addition, multiplication), then integers can be defined as the subset containing them and closed under addition/subtraction. –  Nov 11 '20 at 14:55
  • To your questions (i) I dont know what they look like. (ii) I know that they map sets to another. – Bobby Nov 11 '20 at 18:58
  • I should've have been more specific also. My function f ihas be a first order formula. – Bobby Nov 11 '20 at 19:00

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