  Recently, the Elementary Process Theory (EPT) has been developed as a set of
fundamental principles that might underlie a gravitational repulsion of matter
and antimatter. This paper presents set matrix theory (SMT) as the foundation
of the mathematical-logical framework in which the EPT has been formalized:
Zermelo-Fraenkel set theory (ZF), namely, cannot be used as such. SMT is a
generalization of ZF: whereas ZF uses only sets as primitive objects, in the
framework of SMT finite matrices with set-valued entries are objects sui
generis, with a one-by-one set matrix [x] being identical to the set x. It is
proved that every set that can be constructed in ZF can also be constructed in
SMT: as a mathematical foundation, SMT is thus not weaker than ZF. In addition,
it is shown that SMT is more suitable han ZF for the intended application to
physics. The conclusion is that SMT, contrary to ZF, is acceptable as the
mathematical-logical foundation of the framework for physics that is determined
by the EPT.
