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How do I prove that finite Stars are not defined in First Order Logic

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#first-order-logic #predicate-logic
74
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A question about the use of successions in the quantifier clause of the definition of satisfaction

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#logic #first-order-logic #predicate-logic #quantifiers
55
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Proving a result similar to the diagonal lemma/fixed-point theorem

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#logic #first-order-logic #predicate-logic #peano-axioms #incompleteness
30
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Proving $PAE ⊢ (Pr_S(\#(X → Y)) → (Pr_S(\#(X)) → Pr_S(\#(Y))))$, where $Pr_S(n)$ holds iff $n$ is the Gödel number of a formula provable from $S$

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#logic #first-order-logic #predicate-logic #peano-axioms #incompleteness
163
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Explanation of inference rules with quantifiers

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#logic #propositional-calculus #first-order-logic #predicate-logic
102
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Invertibility of inference rules with quantifiers

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#logic #propositional-calculus #first-order-logic #predicate-logic
37
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Writing a complicated statement with quantifiers.

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#predicate-logic #quantifiers
33
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Translating "All humans have a father" into propositional logic

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#predicate-logic
151
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If $\Gamma \vdash \phi$ then $\Gamma[v / c] \vdash \phi[v / c]$

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#logic #predicate-logic
39
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Logic - equivalence between sentences

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#logic #predicate-logic
203
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Upward Löwenheim-Skolem Theorem for logics without equality

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#logic #predicate-logic #model-theory
101
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Is it true that the domain of this function is finite?

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#functions #logic #predicate-logic #computability #quantifiers
71
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Intuition behind $\exists x \in S, \forall y \in \emptyset, P(x)$

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#proof-writing #predicate-logic
140
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Constructing a model of non-negative integers $\mathbb{N}$

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#logic #set-theory #predicate-logic #model-theory #natural-numbers
89
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Distributing quantifiers across implication

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#logic #predicate-logic

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