Editing Nonfirstorderizability (section)

=== Other examples ===
* The concept of [[identity (philosophy)|identity]] cannot be defined in first-order languages, merely indiscernibility.<ref>{{Cite SEP |url-id=identity|title=Identity|last=Noonan|first=Harold|last2=Curtis|first2=Ben|date=2014-04-25|section=2 "The Logic of Identity"}}</ref>
* The [[Archimedean property]] that may be used to identify the real numbers among the [[real closed field]]s.
* The [[compactness theorem]] implies that [[graph connectivity]] cannot be expressed in first-order logic.{{clarify|date=June 2018}}