The Löwenheim-Skolem-based evidence (P3) establishes cardinality distinctions between models, not that the formulas themselves are irreducibly non-equivalent across all interpretations.

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Formulas(as different versions of Kant's moral law): In Kant's ethics, these are different ways of stating the same moral rule—like saying 'don't lie' versus 'treat people fairly' might express the same underlying principle.
Interpretations(sentences might be true in some interpretations but not others): Different ways of understanding or reading what the symbols and sentences in a logical system mean.
Irreducibly non-equivalent(as used in logic and philosophy of language): Fundamentally or essentially different in meaning in a way that cannot be simplified or reduced; things that cannot be made equivalent no matter how you interpret them.
Löwenheim-Skolem(as used in mathematical logic): A famous theorem in logic stating that if a set of logical rules can describe something, then those same rules can also describe things of wildly different sizes (like describing both tiny and infinite versions of the same structure).

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