`strict_arith_universal_initial`

definition

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module: IndisputableMonolith.Foundation.UniversalForcing.Strict.Invariance
domain: Foundation
line: 18 · github
papers citing: none yet

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IndisputableMonolith.Foundation.UniversalForcing.Strict.Invariance on GitHub at line 18.

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depends on

formal source

  15
  16/-- Every strict realization's derived forced arithmetic is canonically
  17equivalent to `LogicNat`. -/
  18def strict_arith_universal_initial (R : StrictLogicRealization) :
  19    (StrictLogicRealization.arith R).peano.carrier ≃ ArithmeticFromLogic.LogicNat :=
  20  (StrictLogicRealization.toLightweight R).orbitEquivLogicNat
  21
  22/-- **Strict Universal Forcing.**
  23
  24For any two strict Law-of-Logic realizations, the arithmetic derived from
  25their native law data is canonically equivalent. -/
  26noncomputable def strict_universal_forcing (R S : StrictLogicRealization) :
  27    (StrictLogicRealization.arith R).peano.carrier
  28      ≃ (StrictLogicRealization.arith S).peano.carrier :=
  29  ArithmeticOf.equivOfInitial (StrictLogicRealization.arith R)
  30    (StrictLogicRealization.arith S)
  31
  32/-- The Peano surface for every strict realization. -/
  33theorem strict_peano_surface (R : StrictLogicRealization) :
  34    ArithmeticOf.PeanoSurface (StrictLogicRealization.arith R) :=
  35  StrictLogicRealization.peano_surface R
  36
  37end Invariance
  38end Strict
  39end UniversalForcing
  40end Foundation
  41end IndisputableMonolith

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