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Proving this sequent using natural deduction

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#logic #first-order-logic #predicate-logic #quantifiers #natural-deduction
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Does Gödel's theorem rule out derivations from all possible logical systems or just first-order logic?

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#arithmetic #first-order-logic #incompleteness #peano-axioms
379
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Discrete mathematics, antecedent and subsequent of an implication logic

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#discrete-mathematics #logic #first-order-logic
138
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Are there "structure-specific" logical axiomatic systems? Do these have extra power?

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#logic #arithmetic #first-order-logic #incompleteness #peano-axioms
33
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How to express statement in $\mathcal{L}_A$?

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#logic #first-order-logic
86
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Proving complicated predicate calculus sequent

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#logic #first-order-logic #predicate-logic #quantifiers #natural-deduction
281
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Where does $\forall xP(x,x)\land\forall x\forall y( P(x,y)\rightarrow\forall z( P(x,z)\land P(y,z) ) )\rightarrow \exists x\forall yP(y,x)$ not hold?

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#logic #first-order-logic
387
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Negation of uniqueness quantification in first-order logic

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#logic #first-order-logic #quantifiers
98
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Show that Skolemization preserves satisfiability

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#logic #computer-science #first-order-logic #predicate-logic #model-theory
64
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How to know how many models of certain size does a given theory has?

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#logic #first-order-logic #model-theory
2.7k
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Set theoretic concepts in first order logic

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#logic #first-order-logic #foundations #philosophy
84
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Deduction of $\vdash \exists x (Px \rightarrow \forall y Py)$

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#logic #first-order-logic #formal-proofs
103
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Boolean law on predicate logic

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#first-order-logic #predicate-logic
248
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Hilbert style axiom system without generalisation

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#logic #first-order-logic #predicate-logic #proof-theory #hilbert-calculus
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With this definition of completeness, Gödel's Incompleteness result seems not surprising, so why it was back then?

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#logic #first-order-logic #incompleteness

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