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 corresponding dividing lines are those for total transcendentality, superstability and stability.
A complete first-order theory T is called totally transcendental if every formula has bounded Morley rank, i.e. if RM(φ) < ∞ for every formula φ(x) with parameters in a model of T, where x may be a tuple of variables.
This includes complete theories of vector spaces or algebraically closed fields.
These invariants satisfy the inequalities When |T| is countable the 4 possibilities for its stability spectrum correspond to the following values of these cardinals: