Toposes in General Theory of Relativity

Details Toposes in General Theory of Relativity Toposes in General Theory of Relativity

1996-10-31

arxiv.org/abs/gr-qc/9610073v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, LATEX, email guts@univer.omsk.su, grinkev@univer.omsk.su

Scientific paper

We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein theory of space-time. This is a new theory of space-time, created in a purely logical manner. Four possibitities are investigated: axiomatic approach to causal theory of space-time, the smooth toposes as a models of Theory of Relativity, Synthetic Theory of Relativity, and space-time as Grothendieck topos.

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