ONT Re: Model Theory
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Note 5
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| 1. Introduction
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| 1.2. Model Theory for Sentential Logic (cont.)
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| We now set up the sentential logic as a formal language.
| The symbols of our language are as follows:
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| 1. Connectives '&' (and), '~' (not).
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| 2. Parentheses '(' and ')'.
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| 3. A nonempty set $S$ of sentence symbols.
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| Intuitively, the sentence symbols stand for simple statements,
| and the connectives &, ~ stand for the words used to combine
| simple statements into compound statements. Formally,
| the 'sentences' of $S$ are defined as follows:
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| 1.2.2. [Definition of a 'sentence']
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| 1. Every sentence symbol S is a sentence.
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| 2. If p is a sentence, then (~p) is a sentence.
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| 3. If p, q are sentences, then (p & q) is a sentence.
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| 4. A finite sequence of symbols is a sentence
| only if it can be shown to be a sentence by
| a finite number of applications of (1, 2, 3).
|
| Chang & Keisler, 'Model Theory', page 5.
|
| C.C. Chang and H.J. Keisler, 'Model Theory',
| North-Holland, Amsterdam, Netherlands, 1973.
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