FOM: omega-logic

[Neil Tennant]

On Fri, 12 Jul 2002, Fredrik [iso-8859-1] Engström wrote:

> Does anyone know a good reference for omega-logic, something like a
> standard reference. With omega-logic I mean first-order logic with an
> extra predicate K and the rule
> 
>    A(0) A(1) ... A(k) ...
> -----------------------------
> \forall x (K(x) \implies A(x))
> 
> I need to know in what degree compactness fails. 

Utterly. No finite subset of {A(0) A(1) ... A(k) ...} implies
\forall x (K(x) \implies A(x)).

Neil Tennant