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If a proposition can never be proven wrong, is it always true?

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#logic #first-order-logic
349
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Infinitely many non-isomorphic models for the successor function

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#logic #model-theory #first-order-logic
683
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Use of the existential quantifier over multiple individuals

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#logic #first-order-logic #quantifiers
1.7k
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Prove that $\lnot (p \implies q)$ is equivalent to $p \land \lnot q$?

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#logic #first-order-logic #natural-deduction
138
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Basic Logical Implication Question

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#logic #first-order-logic
96
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How to find that $\exists !xP(x) \equiv \exists x(P(x) \land \forall y(P(y) \rightarrow y=x))$ when only LHS is given?

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#logic #propositional-calculus #predicate-logic #first-order-logic #quantifiers
203
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Why don't these types of arguments fall under the domain of logic?

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#logic #first-order-logic
83
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Where am I going wrong: verifying a solution to a non-homogenous difference equation

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#linear-algebra #recurrence-relations #first-order-logic #homogeneous-equation
68
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About 1st-order formulas encoding the runtime configurations of some Turing Machine

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#logic #computability #first-order-logic
59
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Logical equivalent of $\phi[x/y]$?

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#logic #first-order-logic #higher-order-logic
63
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Show that $\alpha$ is independent of the set of axioms (First Order Logic)

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#logic #first-order-logic
3k
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How to prove that if $x,y\in(a,b)$, then $|x-y|<b-a$?

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#logic #proof-writing #first-order-logic
33
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Satisfiability of a field axiom, given model

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#logic #first-order-logic
83
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Determine if the following formulas are logic axioms (First Order Logic)

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#logic #first-order-logic
1.2k
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Are $(\Bbb R,+)$ and $(\Bbb Q, +)$ elementary equivalent?

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#logic #model-theory #first-order-logic

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