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Stating well-foundedness in first-order logic

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Is this reasoning valid or not?

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98
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Equivalent algebraic theory with at most binary operations

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From first-order logic to natural language

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85
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Existential quantifier versus Universial quantifier, from a natural language perspective

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248
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Transform to Prenex Normal Conjunctive Form

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546
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Natural deduction proof - problem with existential elimination

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78
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In first order logic, given F℩xFx, are you able to use alphabetical variation?

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166
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Resolution Principle in First Order Logic

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Open and closed implication formula

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166
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Problems with recursive definitions

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488
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Exercise about Logical Consequences in First Order Logic

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362
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Proving $y = x + 1$ doesn't have a quantifier-free formula in $(\mathbb{Z}, =, <)$

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320
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How to prove statements in formal set theory? Substitution, the empty set and an example.

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On removing/replacing (?) quantifiers in predicate logic

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