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sav08:lecture10 [2008/03/20 11:19] vkuncak |
sav08:lecture10 [2008/03/20 12:25] vkuncak |
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| [[Preliminary Discussion on Models]] | [[Preliminary Discussion on Models]] | ||
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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 model of particular sort. Then it suffices to look into those models. | ||
| [[Ground Terms]] | [[Ground Terms]] | ||
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| [[Herbrand's Expansion Theorem]] | [[Herbrand's Expansion Theorem]] | ||
| - | [[Semidecision Procedure for First-Order Logic without Equality]] | + | [[Semidecision Procedure for First-Order Logic (without Equality)]] |
| - | [[Undecidability of First-Order Logic]] | + | [[Compactness for First-Order Logic]] |
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| - | [[Incorporating Equality]] | + | |
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| - | [[Theorems on Cardinalities of Models]] | + | |
| [[Complete Recursive Axiomatizations]] | [[Complete Recursive Axiomatizations]] | ||
| - | [[Compactness for First-Order Logic]] | + | [[Incorporating Equality]] |
| ===== Resolution in First-Order Logic ===== | ===== Resolution in First-Order Logic ===== | ||