Skolem's original (1933) construction of non-standard arithmetic was intended to show the indeterminacy of the natural number concept, not to populate models with a new category of object.

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Natural numbers(mathematics): The counting numbers: 1, 2, 3, 4, and so on (sometimes including 0, depending on context).
Skolem: # Skolem Skolem refers to Thoralf Skolem, a Norwegian mathematician (1887-1963) who made important discoveries in logic and the foundations of mathematics. He's best known for the "Löwenheim-Skolem theorem," which essentially states that if a mathematical statement can be true in one infinite structure, it can also be true in a simpler, countably infinite structure—a surprising result that challenged assumptions about the nature of mathematical truth. His work fundamentally shaped modern logic and showed surprising limitations in how precisely mathematical languages can describe reality.
indeterminacy(Decision-making under uncertainty in political and legal contexts): Uncertainty or lack of definite knowledge afflicting one or more conditions of a decision procedure, making it impossible to fully specify choices and their outcomes
models(models of global democracy)

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