The Universe from Nothing: A Mathematical Lattice of Empty Sets

Major principles of mathematical constitution of space and the principles of construction of physical space are presented. The existence of a Boolean lattice with fractal properties originating from nonwellfounded properties of the empty set is demonstrated. Space-time emerges as an ordered sequence of mappings of closed 3-D Poincaré sections of a topological 4-space-time provided by the lattice of primary empty cells. The fractal kernel stands for a particle and the reduction of its volume is compensated by morphic changes of a finite number of surrounding cells. Quanta of distances and quanta of fractality are demonstrated. Deformation attributes associated to mass determine the inert mass and the gravitational effects, but fractal deformations of cells are responsible for such characteristics as spin and charge.