ONT Re: Model Theory
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Note 18
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| 1. Introduction
|
| 1.2. Model Theory for Sentential Logic (cont.)
|
| We conclude with a table which summarizes
| the semantical and syntactical notions that
| we have shown to be equivalent (some of these
| are done in the exercises).
|
| Table 1.2.1
| o-----------------------------o-----------------------------o
| | Syntax | Semantics |
| o-----------------------------o-----------------------------o
| | | |
| | p is a tautology | p is valid |
| | | |
| | |- p | |= p |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | !S! is consistent | !S! is satisfiable |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | p is inconsistent | p is refutable |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | p is deducible from !S! | p is a consequence of !S! |
| | | |
| | !S! |- p | !S! |= p |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | p is equivalent to | p is increasing and |
| | a positive sentence | not valid or refutable |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | p is equivalenct to | p is preserved |
| | a conditional sentence | under intersections |
| | | |
| o-----------------------------o-----------------------------o
|
| Chang & Keisler, 'Model Theory', page 16.
|
| C.C. Chang and H.J. Keisler, 'Model Theory',
| North-Holland, Amsterdam, Netherlands, 1973.
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¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
Note 18
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| 1. Introduction
|
| 1.2. Model Theory for Sentential Logic (cont.)
|
| We conclude with a table which summarizes
| the semantical and syntactical notions that
| we have shown to be equivalent (some of these
| are done in the exercises).
|
| Table 1.2.1
| o-----------------------------o-----------------------------o
| | Syntax | Semantics |
| o-----------------------------o-----------------------------o
| | | |
| | p is a tautology | p is valid |
| | | |
| | |- p | |= p |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | !S! is consistent | !S! is satisfiable |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | p is inconsistent | p is refutable |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | p is deducible from !S! | p is a consequence of !S! |
| | | |
| | !S! |- p | !S! |= p |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | p is equivalent to | p is increasing and |
| | a positive sentence | not valid or refutable |
| | | |
| o-----------------------------o-----------------------------o
| | | |
| | p is equivalenct to | p is preserved |
| | a conditional sentence | under intersections |
| | | |
| o-----------------------------o-----------------------------o
|
| Chang & Keisler, 'Model Theory', page 16.
|
| C.C. Chang and H.J. Keisler, 'Model Theory',
| North-Holland, Amsterdam, Netherlands, 1973.
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