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Why does the converse of the Isomorphism Theorem in first-order logic not hold?

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#first-order-logic #solution-verification #predicate-logic #model-theory #metalogic
117
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Understanding compactness theorem on modeling a sentence

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#logic #compactness #first-order-logic #model-theory
177
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Floor or Ceiling Function encoding in First Order logic?

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#first-order-logic #ceiling-and-floor-functions
287
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If a set of sentences $\Gamma$ has an infinite model, then it has a denumerable model too?

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#logic #first-order-logic #solution-verification #model-theory
70
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what would be the FOL of this: "Happy people have exciting lives"

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#first-order-logic
118
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Prove that $\; U\setminus A = U \iff A=\emptyset\; $ where $U$ is the universe (False proof of the opposite).

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#elementary-set-theory #logic #first-order-logic #predicate-logic #fake-proofs
1k
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Universal generalization proof

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#logic #first-order-logic #predicate-logic #quantifiers
200
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Witness property implies scapegoat theory in first-order logic

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#logic #first-order-logic #model-theory
70
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Prove that given any two consecutive integers, one is even and the other is odd.

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#discrete-mathematics #first-order-logic #solution-verification #natural-deduction
182
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Construct a sentence in the empty language.

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#logic #first-order-logic #predicate-logic
170
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Why is $f(x)$ not a variable? (first order logic)

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#logic #first-order-logic
417
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What does this $\models$ $\phi$ mean?

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#logic #notation #first-order-logic #model-theory
32
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Craig Interpolation for first order sentence

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#first-order-logic
1.2k
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Resolution refutation question confused

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#logic #propositional-calculus #first-order-logic
67
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Can every implication $∀x, p(x)→q(x)$ be read as "every $p(x)$, $q(x)$" or "All $p(x)$, are $q(x)$"..

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#logic #soft-question #terminology #first-order-logic

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