Cognizance
发表于 2025-3-25 05:06:26
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Lipoprotein
发表于 2025-3-25 09:02:12
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nitric-oxide
发表于 2025-3-25 14:47:17
Semantics:Making Sense of the SymbolsThere are two different views on a given set of formulae ϕ, namely the syntactical view and the semantical view.
无力更进
发表于 2025-3-25 15:58:40
Maximally Consistent ExtensionsThroughout this chapter, we require that all formulae are written in Polish notation and that the variables are among v0; v1; v2; : : : Notice that the former requirement is just another notation which does not involve brackets, and that by the Variable Substitution Theorem 2.12, the latter requirement gives us semantically equivalent formulae.
GREEN
发表于 2025-3-25 22:28:24
The Completeness TheoremAs in the previous chapter, we require that all formulae are written in Polish notation and that the variables are among v0, v1, v2, . . . Furthermore, let L be a countable signature, let T be a consistent L -theory, and let σ0 be an L -sentence which is not provable from T.
肿块
发表于 2025-3-26 03:10:46
Language Extensions by DefinitionsSometimes it is convenient to extend a given signature L by adding new non-logical symbols which have to be properly deffned within the language L or with respect to a given L-theory T.
母猪
发表于 2025-3-26 04:34:23
Countable Models of Peano ArithmeticBy Gӧdel’s Completeness Theorem 5.5 we know that every consistent theory T has a model, and if T has an infinite model, then it also has arbitrarily large models.
blight
发表于 2025-3-26 11:12:07
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Hectic
发表于 2025-3-26 16:14:42
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兽群
发表于 2025-3-26 19:29:02
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