Can we express the following property of natural numbers as FOL. The property given below is only indicative, I am more interested in knowing how the concepts such as "infinitely many X exists for so and so" can be expressed in FOL. Also these need to be expressed as uninterpreted functions.



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> "For every natural number n, there are infinitely many other natural numbers such that the greatest common divisor of n and each of these other numbers is 1" 
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As I said if you can't express this sentence in FOL at least suggest links/material where I can get leads.



Natural number properties as uninterpreted functions in first order logic
If $f(n)$ is a predicate in the first order language of arithmetic,
then "there are infinitely many $n$ such that $f(n)$ holds" can be
expressed as
$$\forall m\in\mathbb{N}\ \exists k\in\mathbb{N}:f(m+k+1).$$


