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Different definitions on closure under logical consequence

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Is there a finite set of sentences, $\Gamma$ which is satisfiable?

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Monotonicity property of logical systems

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Every finite subset of $\Gamma$ is consistent implies $\Gamma$ is consistent

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Compound Quantifier

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Prove there's no such algorithm

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why is $\forall x (p(x) \implies q(x)) \not\equiv (\forall x p(x)) \implies (\forall x q(x))$

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Is this conclusion via rules of inference correct?

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Express the statement using predicates and quantifiers.

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Logic: Who doesn't eat meat, is vegetarian

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261
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Negation of double universal quantifications

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What is the negation of ∀x∃y¬P(x,y) without using ¬?

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How can I express each of these quantifications in English?

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61
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Predicate logic: $(\forall x\varphi \rightarrow \forall x\psi ) \nRightarrow (\forall x(\varphi \rightarrow \psi))$

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71
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Using separators as functional symbols in first order logic

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