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Is this sentence symbolication correct? Predicate logic

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Which of the three negation of my statement is correct?

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31
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Using axioms of K(n+1) as hypothesis in Kn

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#predicate-logic #first-order-logic
298
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How can I formalize the following sentence into first-order logic?

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Structure for a complete theory

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221
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Why I cannot use universal instantiation rule here?

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75
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Construct a predicate for $x \leqslant y$ given the set of $\mathbb{R}$ or $\mathbb{Z}$ and the symbols $0, 1, +, \cdot, =$

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76
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Non-negativity of an integer

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1.1k
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"Everybody Loves a Lover" Isn't Z part of Everybody?

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190
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Can induction be logically derived?

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444
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Hilbert-Bernays theorem

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Translating sentence to FOL question

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74
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Must a predicate $P(x)$ be dependent on its variables?

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999
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FOL to English translation questions.

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424
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Henkin/branching quantifier: say what?

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