Stability Spectrum
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In model theory, a branch of mathematical logic, a complete first-order theory T is called stable in (an infinite cardinal number), if the Stone space of every model of T of size has itself size . T is called a stable theory if there is no upper bound for the cardinals such that T is stable in . The stability spectrum of T is the class of all cardinals such that T is stable in . For countable theories there are only four possible stability spectra. The corresponding d...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In model theory, a branch of mathematical logic, a complete first-order theory T is called stable in (an infinite cardinal number), if the Stone space of every model of T of size has itself size . T is called a stable theory if there is no upper bound for the cardinals such that T is stable in . The stability spectrum of T is the class of all cardinals such that T is stable in . 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.
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