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  "body": "\n## Summary\n\nA complete theory is stable when its models have few [[types|9V71Q3SD1G]].\nFor some infinite cardinal $\\lambda$, every parameter set of size $\\lambda$ has at most $\\lambda$ complete types over it.\nEquivalently, no formula can define an infinite linear order on tuples, a condition called the order property.\nStable theories, introduced and developed by Saharon Shelah, admit a good theory of independence and dimension.\nAlgebraically closed fields, vector spaces and modules give stable theories, while dense linear orders and real closed fields do not.\n\n## Explanations\n\n### L1 human\n\nStability measures how complicated the possible behaviours of elements in a theory are.\nIn a stable theory, fixing a set of parameters leaves relatively few ways for a new element to sit relative to them.\nIn the rational numbers with their order, every cut of a countable set gives a different behaviour, so there are too many, and the theory is unstable.\nIn algebraically closed fields, a new element is either algebraic over the parameters, in finitely many ways for each polynomial, or transcendental, and this keeps the count small.\n",
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