**Stability Spectrum**

In model theory, a branch of mathematical logic, a complete first-order theory *T* is called **stable in λ** (an infinite cardinal number), if the Stone space of every model of *T* of size ≤ λ has itself size ≤ λ. *T* is called a **stable theory** if there is no upper bound for the cardinals κ such that *T* is stable in κ. The **stability spectrum** of *T* is the class of all cardinals κ such that *T* is stable in κ.

For countable theories there are only four possible stability spectra. The corresponding dividing lines are those for total transcendentality, superstability and stability. This result is due to Saharon Shelah, who also defined stability and superstability.

Read more about Stability Spectrum: The Stability Spectrum Theorem For Countable Theories, The Uncountable Case, See Also

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“The world can be at peace only if the world is stable, and there can be no *stability* where the will is in rebellion, where there is not tranquility of spirit and a sense of justice, of freedom, and of right.”

—Woodrow Wilson (1856–1924)