I am trying to do exercise n.6 on page 229 of "A Course in Universal Algebra" by S.Burris & H.P.Sankappanavar:

"Show that 'being of infinite size' is a first-order property (relative to any K)".

I understand that there must be a first order formula expressing 'being of infinite size', but I do not know how to find it.

Would anybody help me ?

Thank you very much

Am I right if I say:

if

s(x) means successor of x

then (see attachment)