  The new global version of the Cauchy-Kovalevskaia theorem presented here is a
strengthening and extension of the regularity of similar global solutions
obtained earlier by the author. Recently the space-time foam differential
algebras of generalized functions with dense singularities were introduced. A
main motivation for these algebras comes from the so called space-time foam
structures in General Relativity, where the set of singularities can be dense.
A variety of applications of these algebras have been presented elsewhere,
including in de Rham cohomology, Abstract Differential Geometry, Quantum
Gravity, etc. Here a global Cauchy-Kovalevskaia theorem is presented for
arbitrary analytic nonlinear systems of PDEs. The respective global generalized
solutions are analytic on the whole of the domain of the equations considered,
except for singularity sets which are closed and nowhere dense, and which upon
convenience can be chosen to have zero Lebesgue measure. In view of the severe
limitations due to the polynomial type growth conditions in the definition of
Colombeau algebras, the class of singularities such algebras can deal with is
considerably limited. Consequently, in such algebras one cannot even formulate,
let alone obtain, the global version of the Cauchy-Kovalevskaia theorem
presented in this paper.
