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
Famous quotes containing the word stability:
“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 (18561924)