What question did this study set out to answer?

The aim is to characterize the requirements for interpreting unbounded strict linear orders in finite relational structures using first-order logic.

January 18, 2026Open Access

Diekens Law: Symmetry, Prerequisite Anchors, and Comparison Mass in Finite First-Order Interpretations

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Finite model theory demonstrates structural requirements for interpreting strict linear orders, suggesting key limitations.

The aim is to characterize the requirements for interpreting unbounded strict linear orders in finite relational structures using first-order logic.
Introduced Diekens Law as a foundational result.
Proved necessity results regarding interpretation requirements.
Classified structural changes with variations in logical strength.
Defined a symmetry-breaking anchor is necessary for unbounded interpretations.
Demonstrated quadratic witness mass is required in FO-local comparison.
Showed witness mass can collapse to linear size in FO with transitive closure.

Kearon Allen (2026) studied this question.

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