IndisputableMonolith.Foundation.UniversalForcing.StrictRealization
This module defines strict Law-of-Logic realizations that carry only native law data and omit any supplied orbit. Workers on the Universal Forcing theorem cite it when they need the minimal structure before adding domain-specific content. The module consists of definitions and interpretation maps that prepare the ground for admissible classes and positive-ratio constructions.
claimA strict realization is a structure whose fields are the propositions excluded_middle_law, composition_law and invariance_law, together with interpretation maps to arithmetic objects, with no external orbit supplied.
background
The parent UniversalForcing module states that any two Law-of-Logic realizations yield canonically equivalent forced arithmetic objects because those objects are initial Peano algebras. The present module restricts attention to the strict case in which the three law propositions are carried as raw Props and no orbit is furnished from outside. Sibling definitions include StrictLogicRealization, FreeOrbit, interpret, interpret_zero, interpret_step, toLightweight, arith and peano_surface.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the StrictLogicRealization structure that AdmissibleClass uses to treat the five domain realizations as trivial instances of the law propositions, and that PositiveRatio uses to construct the strict continuous positive-ratio realization directly from SatisfiesLawsOfLogic. It therefore closes the gap between the abstract Universal Forcing statement and the concrete admissible-class and positive-ratio applications.
scope and limits
- Does not instantiate the law propositions for any concrete domain.
- Does not supply orbit data or external models.
- Does not contain the quantified universal-forcing statements.
- Does not prove associativity or decidability of the laws.