[FOM] SOL vs. ZFC

[José Ferreirós Domínguez]

Let me add something: when I wrote, "The standard semantics of SOL must be Henkin semantics", that was an oversimplification. Proof theorists have long been employing SOL in ways that are perfectly Ok, as far as I can see, but different from Henkin's. The key is just the rejection of any special status to "full" semantics, plus the arguments why this goes too far from logic.

Again, there's no problem in working with hybrid systems. But the realization that SOL set-theoretically interpreted can support quite a lot of mathematics is no insight into logic and its connections with mathematics.

Best, Jose

Prof. Jose Ferreiros
Departamento de Filosofia y Logica
Universidad de Sevilla
http://personal.us.es/josef/