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Defining a formula inductively using structural induction

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#logic #induction #propositional-calculus
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Is it a paradox if I prove something as unprovable?

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#logic #proof-theory #peano-axioms
101
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A productive set contains an infinite r.e. set.

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#logic #computability
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Use the well-ordering principle to prove that every integer $n\ge2$ has a prime factor.

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#elementary-set-theory #proof-verification #logic #proof-writing #well-orders
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Is there a *simple* example of how the axiom of choice can lead to a counterintuitive result?

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#logic #model-theory #axiom-of-choice
260
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Are any of the counterintuitive functions whose existence is postulated by the axiom of choice computable?

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#logic #set-theory #computability #axiom-of-choice #set-partition
61
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What does $C,D \models \delta$ mean?

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#logic #first-order-logic #model-theory
39
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Laws of Logic Expression

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#logic #propositional-calculus #boolean-algebra
274
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Prove a function is functionally complete/incomplete

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#logic #boolean-algebra
1.8k
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Primitive propositions in Propositional Logic

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#logic #propositional-calculus
104
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How can this be a tautology?

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#discrete-mathematics #logic #propositional-calculus
69
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Logical Statements involving the definition of Separability

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#general-topology #functional-analysis #logic #metric-spaces
75
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Is the formula $\exists x : x^2-a=0$ not downward absolute over the theory of field of rational numbers?

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#logic #model-theory
77
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Proving that the number of atoms in a formula is equal to the number of the symbols $\land,\lor,\rightarrow$ plus 1

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#logic #propositional-calculus
32
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How to simplify $\bar{X_1}\cup(\bar{X_2}\setminus(X_3\cap\bar{X_1})$?

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#elementary-set-theory #logic

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