First order meta theories
A Hutchinson · Logic Journal of IGPL · 1997
Ian Mason [25] has shown that the meta-theory of propositional calculus is not axiomatizable. That is not to say that its meta-theory cannot be studied. There may be a sequence of theories, indexed by the ordinals, which encompass the entire meta-theory. The same goes for other forms of logic too. Herein is proposed one candidate for such a sequence, for a wide range of logics.