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Why is the following statement involving predicates false?

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First order theories with open formulas as axioms

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If $R$ is $\Sigma_n$ and $(x,y)\in A\iff (\forall z < y) R(x,y,z)$, then $A$ is $\Sigma_n$

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#logic #predicate-logic #computability #quantifiers
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Confusion about writing $Inf$ as a $\Pi_2$ set

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151
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Question about empty set uniqueness proof using Set Existence, Extensionality, and the Comprehensive Schema.

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#set-theory #predicate-logic
302
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How do I reason with Skolem functions?

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707
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Necessary but not sufficient

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54
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What interpretation shows that $\forall y \;\exists x(Fxy)$ does not imply $\exists x \;\exists y(Fxy \wedge Fyx)$?

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#predicate-logic
258
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help negating statements (exclusive or)

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#discrete-mathematics #logic #predicate-logic
51
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A Question About Predicate Logic

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#discrete-mathematics #propositional-calculus #predicate-logic
29
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How to derive: $\left(\forall x\right)\left[Lx\rightarrow\left(Mx\land N x\right)\right]\vdash\left(\forall x\right)\left(Lx\rightarrow M x\right)$

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#solution-verification #first-order-logic #predicate-logic
346
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Difficulty in understanding predicate symbols in FOL

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141
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Conceptual question about universal generalization and the domain of discourse of our "arbitrary elements"

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#logic #first-order-logic #predicate-logic
150
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How to represent the following in predicate logic

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107
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When does $A$ iff $B$, imply $A=B$?

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#logic #first-order-logic #predicate-logic #type-theory

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