`arith_universal_initial'`

definition

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module: IndisputableMonolith.Foundation.UniversalForcing.Invariance.Universal
domain: Foundation
line: 21 · github
papers citing: none yet

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IndisputableMonolith.Foundation.UniversalForcing.Invariance.Universal on GitHub at line 21.

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depends on

formal source

  18
  19/-- Every realization's forced arithmetic is canonically equivalent to the
  20reference `LogicNat` Peano object. -/
  21noncomputable def arith_universal_initial' (R : LogicRealization) :
  22    (arithmeticOf R).peano.carrier ≃ ArithmeticFromLogic.LogicNat :=
  23  R.orbitEquivLogicNat
  24
  25/-- **Universal Forcing Meta-Theorem.**
  26
  27For any two Law-of-Logic realizations, the forced arithmetic objects are
  28canonically equivalent. -/
  29noncomputable def universal_forcing (R S : LogicRealization) :
  30    (arithmeticOf R).peano.carrier ≃ (arithmeticOf S).peano.carrier :=
  31  ArithmeticOf.equivOfInitial (arithmeticOf R) (arithmeticOf S)
  32
  33/-- Peano surface is available for every realization's forced arithmetic. -/
  34theorem universal_peano_surface (R : LogicRealization) :
  35    ArithmeticOf.PeanoSurface (arithmeticOf R) :=
  36  peano_surface R
  37
  38end Universal
  39end Invariance
  40end UniversalForcing
  41end Foundation
  42end IndisputableMonolith

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