A semantics for a weak free logic.
Ermanno Bencivenga · Notre Dame Journal of Formal Logic · 1978
We know that, if in a common system of standard quantification and identity theory, such as the one having (AO) A, where A is a tautologywhere A is an axiom 2 as axiom-schemata and (Rl) If A and A 3 B are theorems, then B is a theorem as rule of inference, we drop the Principle of Specification (i.e., (Al)), we are able to obtain as a theorem the following weaker variant of the same principle: (Al') (VΛΓΛ & 3x(x = a)) => A a /x.*