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sav08:preliminary_discussion_on_models [2008/03/20 11:22] vkuncak |
sav08:preliminary_discussion_on_models [2008/03/20 11:23] vkuncak |
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| ====== Model Sizes ====== | ====== Model Sizes ====== | ||
| - | We saw: if formula has a model of some size, it has many models of same size, from [[Isomorphisms of Interpretations]]. | + | We saw: if formula has a model of some size, it has many models of same size, from [[Isomorphism of Interpretations]]. |
| Are there first-order formulas that have only finite models? | Are there first-order formulas that have only finite models? | ||
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| What is the cardinality of the models we need to consider? There are many useful models whose domains is not a [[countable set]]. | What is the cardinality of the models we need to consider? There are many useful models whose domains is not a [[countable set]]. | ||
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| + | Difficulty in checking $\models S$: there are infinitely many models, of arbitrarily large cardinalities. | ||
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| + | Goal: show that if a set $S$ of formulas has a model, then it has a particular kind, and this model is countable. | ||
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