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A curious logical formula involving prime numbers

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#logic #first-order-logic
45
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Is there any true interpretation of the sentence $\forall x \forall y$ $((P(x) \wedge P(y)) \wedge (x \neq y))$

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#first-order-logic
172
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First orderer logic completeness and independence: the proof that disappear?

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#logic #first-order-logic #model-theory #independence #proof-theory
176
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How to write in second-order logic that a relation is divisible by another?

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#logic #first-order-logic #second-order-logic
188
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Injective homomorphism that isn't a strong homomorphism

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#first-order-logic
183
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Substitution Theorem on "A Concise Introduction to Mathematical Logic" by W. Rautenberg

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#logic #first-order-logic #predicate-logic #substitution
306
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Is there a proof of $\lnot \forall x, P(x) \iff \exists x, \lnot P(x)$

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#logic #first-order-logic #predicate-logic #quantifiers #formal-proofs
2.3k
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Can anyone clarify the rules for $\forall$ intro and elimination, and $\exists$ intro and elimination?

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#logic #proof-writing #first-order-logic #quantifiers #natural-deduction
65
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Translating set syntax in FOL

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#elementary-set-theory #definition #first-order-logic #predicate-logic #quantifiers
20
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Centered family in a Boolean algebra

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#definition #first-order-logic
323
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Are quantifiers only required because of infinite proposition chains?

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#logic #soft-question #definition #first-order-logic #quantifiers
113
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A question on the formality of a theory

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#logic #first-order-logic #predicate-logic #formal-languages
229
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Need help understanding variable label/scoping rules for first order logic

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#logic #first-order-logic #predicate-logic #quantifiers #convention
154
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Quantifier order confusion

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#proof-verification #logic #first-order-logic #quantifiers
131
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Is this a free variable? Something else?

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#logic #definition #first-order-logic #quantifiers

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