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Enough Model Theory to Understand Skolem’s “Paradox”

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This article seeks to describe some of the basic foundations of mathematics from a model-theoretic perspective with the goal of obtaining the “Downward Löwenheim–Skolem” theorem.  After the theorem is introduced the seemingly paradoxical nature of it is discussed.
University Library System, University of Pittsburgh
Title: Enough Model Theory to Understand Skolem’s “Paradox”
Description:
This article seeks to describe some of the basic foundations of mathematics from a model-theoretic perspective with the goal of obtaining the “Downward Löwenheim–Skolem” theorem.
  After the theorem is introduced the seemingly paradoxical nature of it is discussed.

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