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sav08:lecture10 [2008/03/20 11:19] vkuncak |
sav08:lecture10 [2008/03/20 12:27] 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]] |
[[Incorporating Equality]] | [[Incorporating Equality]] | ||
- | [[Theorems on Cardinalities of Models]] | + | ===== Undecidability and Incompleteness ===== |
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+ | [[Undecidability of First-Order Logic]] | ||
[[Complete Recursive Axiomatizations]] | [[Complete Recursive Axiomatizations]] | ||
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- | [[Compactness for First-Order Logic]] | ||
===== Resolution in First-Order Logic ===== | ===== Resolution in First-Order Logic ===== |