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Is this theorem equivalent to "existential instantiation" rule?

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90
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Showing that $\neg[ Px\rightarrow \forall xPx]\vdash \forall xPx$ via generalization theorem

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37
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Sentences of FOL related by the substitution of individual constants

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#first-order-logic
370
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How to prove that $\Gamma\vdash\forall x\psi$ if $x$ occurs free in $\Gamma$, via generalization theorem?

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128
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On Decidability of first order logic

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Is $\Delta_0=\Delta_1$ in arithmetical hierarchy?

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Online tools for checking validity of classical, intuitionistic, ... logic formulas?

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713
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existential quantifiers equivalence

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715
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Sequent and Gentzen calculus formulae

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2k
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How would you define the set of even numbers in $\mathbb{Z}$ using a first order sentence?

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#logic #model-theory #first-order-logic
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Using first order sentences, axiomize the $\mathcal{L}$-theory of an equivalence relation with infinitely many infinite classes.

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317
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Using first order sentences, how would you write down the axioms of finite field?

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75
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Reference Request: Compendium of Hilbert Systems

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#reference-request #logic #first-order-logic #axioms
415
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Question on Komjáth's "three clouds may cover the plane"

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#set-theory #cardinals #first-order-logic #infinitary-combinatorics
130
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If $\Gamma\cup\{\sim(A\land B)\}$ is consistent, what can be said about $\Gamma\cup\{\sim(A\lor B)\},\Gamma\cup\{\sim A\},\Gamma\cup\{\sim B\}$?

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