FOM: Re: finite axiomatization and conservative extension

[Neil Tennant]

Correction (courtesy of Thomas Forster):

> Could any fom-er supply a reference for the earliest proof of a
> theorem along the following lines?:
> 
> Any r.e. first-order theory in a language L is, for some L*
> extending L, the restriction to L of some finitely axiomatizable
> theory in L*.
> 
> Second question:
> 
> Are there any interesting/natural conditions on such r.e. sets that
> would force L* to be a language of higher order than L, rather than
> merely a first-order extension of L?

Neil Tennant