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Expressibility of Peano arithmetic and the Arithmetical Hierarchy

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#logic #first-order-logic
411
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Arithmetical hierarchy: Why is $\Delta_0^0\ne \Delta_1^0$?

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#logic #first-order-logic
754
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Precise definition of $\Sigma_0^0$ in the arithmetical hierarchy

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#logic #first-order-logic
104
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What are the different ways to get a first-order formula that express the statement"$P$ is the $n$-th prime"

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#logic #prime-numbers #first-order-logic
364
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Natural Deducion: assumptions can be used more than once?

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#logic #first-order-logic #proof-theory #natural-deduction
85
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Citations for the proof of universality of graph classes

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#graph-theory #first-order-logic #symmetric-groups #universal-algebra #universal-property
74
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Using separators as functional symbols in first order logic

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#logic #predicate-logic #first-order-logic
154
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True or falsehood of open formula under a fixed interpretation

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#logic #predicate-logic #first-order-logic
451
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Is $\pi = 3.14159...$ first-order definable in the reals?

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#real-numbers #first-order-logic #pi
42
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can you help me to transform ∀x FO logical formula to it equivalent ¬∃ formula?

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#logic #first-order-logic
125
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Software for solving first-order logic

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#logic #reference-request #first-order-logic #math-software
2.4k
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Contrapositive of the statement involving "for every" and "there exists"

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#predicate-logic #first-order-logic
788
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understanding a proof which uses induction on the length of a formula

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#logic #induction #first-order-logic
68
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Are those statements Tautology?

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#predicate-logic #first-order-logic
65
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Finding equivalent statements with quantifiers

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#elementary-set-theory #first-order-logic

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