Short recursively saturated models and boundedly saturated models
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Short Recursively Saturated Models
A model is short if there is an element in the model whose Skolem closure is cofinal in the model. That is, M is short iff there is a in M such that M=Sup(Scl(a)). If a model is not short, it is called tall.
A type p(v,b) is bounded if it contains the formula v<b.
A model M is boundedly saturated if for every b in M, every bounded recursive type p(v,b) is realized in M.
A model is short recursively saturated if it is short and boundedly saturated.
Every elementary cut of a recursively saturated model is boundedly saturated.
