Abstract:
We describe an algebraic way to code the causal information of a discrete spacetime. The causal set ? is transformed to a description in terms of the causal pasts of the events in ?. This is done by an evolving set, a functor which to each event of ? assigns its causal past. Evolving sets obey a Heyting algebra which is characterised by a non-standard notion of complement. Conclusions about the causal structure of the causal set can be drawn by calculating the complement of the evolving set. A causal quantum theory can be based on the quantum version of evolving sets, which we briefly discuss.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 20 February 1999 / Accepted: 8 November 1999
Rights and permissions
About this article
Cite this article
Markopoulou, F. The Internal Description of a Causal Set:¶What the Universe Looks Like from the Inside. Comm Math Phys 211, 559–583 (2000). https://doi.org/10.1007/s002200050826
Issue Date:
DOI: https://doi.org/10.1007/s002200050826