• A simple characterization of the pseudo-Euclidean space in terms of order (causal) structure (Alexandrov's Problem) (1970 - 1987),
• A description of affine semigroups and their automorphisms of solvable Lie groups (1972-1993),
• A topos-theoretic approach to the foundation of the theory of relativity or causal categorical theory of pseudo-Riemannian manifolds (1990- 1994),
• Estimate of energy of creation of wormholes in space-time (1981),
• Estimate of the physical conditions of existence of time machines in space-time (1973, 1992, 1994),
• The description of symmetry creation in the Universe based on theory of equivariant bordisms (1984),
• The mathematical models of ethnogenesis (1994) and sociogenesis (1995).
• The description of dimension jumps of space and time,
• The mathematical modelling of forest ecological catastrophes
• The multiverse description of antigravitation

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