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Does a theory $(\sim, =)$ admit quantifier elimination?

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#model-theory #quantifiers #quantifier-elimination
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When the occurrence of a variable is said bound or free in a quantified statement?

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#discrete-mathematics #predicate-logic #quantifiers
59
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Interpretation for the predicate formula

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#first-order-logic #predicate-logic #quantifiers
110
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Confusion with contraposition of an implication with quantifiers

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#analysis #logic #proof-writing #quantifiers
145
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Negating a quantified predicate

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#logic #predicate-logic #quantifiers
45
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We can express predicate $x = \alpha$ in the interpretation $(\mathbb{R}, +, =, >, \cdot, 0, 1)$ iff $\alpha$ is algebraic.

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#predicate-logic #quantifiers
69
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Quantifiers implication question

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#logic #predicate-logic #quantifiers
1.8k
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What is null quantification?

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#discrete-mathematics #predicate-logic #quantifiers
3.4k
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Negation of Atleast One

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#logic #quantifiers
726
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Prove using Natural Deduction in predicate logic $(\forall x\ P(x))\to Q ⊢ \exists x (P(x)\to Q)$

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#logic #first-order-logic #quantifiers #natural-deduction #formal-proofs
109
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Is somebody no ones cousin or is somebody not a cousin to everybody?

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#logic #first-order-logic #predicate-logic #quantifiers
320
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A quantifier for "there may exist" (for use in Set Builder notation)

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#quantifiers #alternative-set-theories
212
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Expression logical statements using rules of inference with quantifiers

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#propositional-calculus #predicate-logic #quantifiers
562
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Pushing in negation in first order logic

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#discrete-mathematics #logic #first-order-logic #predicate-logic #quantifiers
243
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What is the difference between $\neg\exists x$ and $\neg\forall x$ ? Is $\neg\exists x$ ever used?

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#logic #first-order-logic #predicate-logic #quantifiers #logic-translation

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