Difference between revisions of "Short recursively saturated models and boundedly saturated models"

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(Short Recursively Saturated Models)
(Short Recursively Saturated Models)
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Every elementary cut of a recursively saturated model is boundedly saturated.
 
Every elementary cut of a recursively saturated model is boundedly saturated.
  
[[Countable Short Recursively Saturated Models]]
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== Countable Short Recursively Saturated Models ==
  
[[Short Saturated Models]]
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== Short Saturated Models ==

Revision as of 19:51, 23 November 2014

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.

Countable Short Recursively Saturated Models

Short Saturated Models