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Toposes in General Theory of Relativity

Alexandr K. Guts·Egor B. Grinkevich
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Abstract

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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Alexandr K. Guts, Egor B. Grinkevich. 1996-10-31. Toposes in General Theory of Relativity. https://arxiv.org/abs/gr-qc/9610073

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