  This paper introduces a new theory which encompasses concepts and ideas from
set theory, type theory, and Le\'{s}niewski's mereology and describes its
possibility as an alternative foundation for mathematics. In the introduction
section I will introduce motives for development of the theory and some remarks
on the methods of presentation. Axioms of the theory and their philosophical
background and justification on the basis of intuitive view are discussed next.
Discussed after are realizations of mathematical concepts such as $\mathbb{N}$,
$\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, etc. Then this paper
concludes with comparisons between the theory and ZFC and its mathematical
limitations.
