  Suppose L = {<, . . .} is any countable first order language in which < is
interpreted as a linear order. Let T be any complete first order theory in the
language L such that T has a kappa-like model where kappa is an inaccessible
cardinal. Such T satisfies the Inaccessibility Scheme. In this paper we study
model theory of the inaccessibility scheme at the level of the existence of
elementary end extensions for various models of it.
