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'Politics', 'Intermediate Logic' and 'On Second-Order Logic'
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7 ideas
5. Theory of Logic / K. Features of Logics / 2. Consistency
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13540
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A set of formulae is 'inconsistent' when there is no interpretation which can make them all true [Bostock]
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13541
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For 'negation-consistent', there is never |-(S)φ and |-(S)¬φ [Bostock]
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13542
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A proof-system is 'absolutely consistent' iff we don't have |-(S)φ for every formula [Bostock]
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5. Theory of Logic / K. Features of Logics / 4. Completeness
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10834
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Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
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5. Theory of Logic / K. Features of Logics / 6. Compactness
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13841
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Why should compactness be definitive of logic? [Boolos, by Hacking]
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13544
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Inconsistency or entailment just from functors and quantifiers is finitely based, if compact [Bostock]
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13618
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Compactness means an infinity of sequents on the left will add nothing new [Bostock]
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