Preservation Theorems
The value of modal companions and the Blok–Esakia theorem as a tool for investigation of intermediate logics comes from the fact that many interesting properties of logics are preserved by some or all of the mappings ρ, σ, and τ. For example,
- decidability is preserved by ρ, τ, and σ,
- finite model property is preserved by ρ, τ, and σ,
- tabularity is preserved by ρ and σ,
- Kripke completeness is preserved by ρ and τ,
- first-order definability on Kripke frames is preserved by ρ and τ.
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—John Locke (1632–1704)