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Why is better to work with first-order Peano's axioms than with second-order Peano's axioms?

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#logic #first-order-logic #peano-axioms #higher-order-logic
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Can someone please explain the difference between first/second/third order logic, using examples?

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#logic #predicate-logic #first-order-logic #higher-order-logic
202
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Is it possible to express Coq Calculus of Constructions in terms of Isabelle/HOL or vice versa?

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#logic #proof-verification #math-software #higher-order-logic #computer-assisted-proofs
292
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Third order logic: quantifying sets of sets or relations of ...?

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#logic #first-order-logic #higher-order-logic
482
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The place of lambda abstraction in internal and Mitchell-Bénabou languages

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#category-theory #topos-theory #lambda-calculus #type-theory #higher-order-logic
81
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Translation of an argument in logical notation.

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#logic #predicate-logic #higher-order-logic
44
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A rule in the recursive clauses governing type formation in a higher order logic

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#logic #type-theory #higher-order-logic
137
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Classifying topos for higher order logic

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#logic #category-theory #topos-theory #higher-order-logic
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Type theory vs higher-order logic

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#logic #terminology #foundations #type-theory #higher-order-logic
121
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Modal logic formulation

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#proof-verification #logic #modal-logic #higher-order-logic
710
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Axioms in Gödel's ontological proof are inconsistent?

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#logic #philosophy #fake-proofs #modal-logic #higher-order-logic
401
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Having trouble Solving fourth order heat equation.

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#partial-differential-equations #heat-equation #higher-order-logic #linear-pde
751
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Why are higher-order logics less well-behaved?

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#logic #higher-order-logic
689
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Availability of logic lectures online

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#logic #soft-question #online-resources #higher-order-logic
231
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Is there such a thing as "second-order-undecidability"? And what about higher order Undecidability statements?

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#logic #higher-order-logic

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