`continuousRealization`

definition

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module: IndisputableMonolith.Foundation.UniversalForcing.ContinuousRealization
domain: Foundation
line: 19 · github
papers citing: none yet

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IndisputableMonolith.Foundation.UniversalForcing.ContinuousRealization on GitHub at line 19.

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formal source

  16open LogicAsFunctionalEquation
  17
  18/-- Continuous positive-ratio Law-of-Logic realization. -/
  19noncomputable def continuousRealization
  20    (C : ComparisonOperator) (h : SatisfiesLawsOfLogic C) :
  21    LogicRealization :=
  22  LogicRealization.ofPositiveRatioComparison C h
  23
  24/-- The continuous realization carries the universal forced arithmetic. -/
  25noncomputable def continuous_arith_equiv_logicNat
  26    (C : ComparisonOperator) (h : SatisfiesLawsOfLogic C) :
  27    (arithmeticOf (continuousRealization C h)).peano.carrier
  28      ≃ ArithmeticFromLogic.LogicNat :=
  29  (continuousRealization C h).orbitEquivLogicNat
  30
  31end ContinuousRealization
  32end UniversalForcing
  33end Foundation
  34end IndisputableMonolith

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