PIRSA:12050049 Scientific Series Quantum Gravity

DOI10.48660/12050049

Series: Quantum Gravity

Bell, J. (2012). Causal Sets and Frame-Valued Set Theory. Perimeter Institute. https://pirsa.org/12050049

Bell, John. Causal Sets and Frame-Valued Set Theory. Perimeter Institute, May. 23, 2012, https://pirsa.org/12050049 

@misc{ pirsa_PIRSA:12050049,
  doi = {10.48660/12050049},
  url = {https://pirsa.org/12050049},
  author = {Bell, John},
  keywords = {Quantum Gravity},
  language = {en},
  title = {Causal Sets and Frame-Valued Set Theory},
  publisher = {Perimeter Institute},
  year = {2012},
  month = {may},
  note = {PIRSA:12050049 see, \url{https://pirsa.org}}
}

Abstract

In spacetime physics any set C of events—a causal set—is taken to be partially ordered by the relation £ of possible causation: for p, q Î C,   p £ q means that q is in p’s future light cone. Fotini Markopoulou has proposed that the causal structure of spacetime itself be represented by “sets evolving over C” —that is, in essence, by the topos Set C of presheaves on Cop.  In this talk I am going to show how Set  C may be effectively replaced by a certain model V(H) of intuitionistic set theory—frame-valued set theory—with (I hope) illuminating results. In particular, Markopoulou’s idea of viewing the universe “from the inside” will amount to placing oneself “inside” V(H). I will also sketch the role played in this framework by covering schemes and sheaves.

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