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A consistent first-order theory whose impredicative second-order variant is inconsistent

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#predicate-logic #first-order-logic #higher-order-logic
920
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Can all math results be formalized and checked by a computer?

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#logic #predicate-logic #first-order-logic #foundations #proof-theory
105
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Not understanding universal generalisation, and proof that uses it

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#predicate-logic #first-order-logic
135
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Can Goodstein's theorem be expressed as an axiom or axiom scheme in PA?

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#logic #predicate-logic #peano-axioms
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Are these logical predicate translations valid?

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#logic #predicate-logic
244
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Help needed with axiomatic deductions

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#predicate-logic #axioms #first-order-logic
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English sentence to FOL

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#logic #predicate-logic #first-order-logic
388
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translate sentences into logic

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#logic #predicate-logic #logic-translation
75
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How to interpret predicate logic if no context is given about possible values of variables?

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#logic #predicate-logic
265
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$\exists \implies \forall$

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#logic #predicate-logic #quantifiers
193
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Logic and mathematical variables as objects

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#logic #arithmetic #predicate-logic
3k
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**Ended Competition:** What is the shortest proof of $\exists x \forall y (D(x) \to D(y)) $?

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#logic #first-order-logic #predicate-logic #alternative-proof #natural-deduction
170
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Hints and/or help needed for axiomatic deduction

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#logic #predicate-logic #first-order-logic
415
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True or false: for all $x$ there is a $y$ such that if $x$ is non negative then $y^2 = x$

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#predicate-logic #real-numbers
53
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Small part of loop invariant i'm not getting

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#predicate-logic #first-order-logic

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