Löwenheim–Skolem Theorem (Countable Model Form)

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In a countable first-order language, a satisfiable theory has a model with at most countably many elements. Skolem's paradox distinguishes an external enumeration from a bijection available inside that model.

Before opening the references

first-order structure · Completeness of First-Order Logic · Countable Set

Where to read

  1. Start here: Sets, Logic, Computation: An Open Introduction to Metalogic

    Richard Zach; based on the Open Logic Text by the Open Logic Project · Open textbook · English · Free full text

    §12.11 The Löwenheim–Skolem Theorem, Theorem 12.32 (finite or countably infinite model) and Example 12.34 (Skolem's Paradox)

    Source page · Checked 2026-10-16

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Model Theory in the library · Preparation and skip guidance

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