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Can second order logic express each (computable) infinitary logic sentence?

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#logic #higher-order-logic
355
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Are there statements in set theory about arithmetic beyond the reach of the analytical hierarchy?

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#logic #set-theory #arithmetic #higher-order-logic
145
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Can we blend logic and set theory into ONE system?

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#logic #set-theory #first-order-logic #higher-order-logic #second-order-logic
222
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Higher order arithmetic, hierarchies and proof theoretic ordinals

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#ordinals #foundations #higher-order-logic #ordinal-analysis
414
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Is it fair to say that ZFC axioms can not even be stated in FOL?

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#logic #set-theory #first-order-logic #foundations #higher-order-logic
198
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Strongly constructive proofs: Proofs that don't make use of decidability?

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#logic #type-theory #constructive-mathematics #intuitionistic-logic #higher-order-logic
178
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d^2y/dy^2 expressed in t

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#multivariable-calculus #derivatives #partial-derivative #chain-rule #higher-order-logic
133
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On a definition in a proof

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#logic #type-theory #lambda-calculus #higher-order-logic
115
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How foundation of mathematics can be based on a first order logic system?

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#first-order-logic #foundations #higher-order-logic
145
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Is the existential quantifier commutative in intuitionistic higher order logic?

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#logic #type-theory #intuitionistic-logic #higher-order-logic
56
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finding the shape of the higher order equations

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#graphing-functions #3d #higher-order-logic
63
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Are more classes of structures axiomatizable as you increase the order of the logic?

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#model-theory #higher-order-logic
114
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Gödel's proof: What if all axioms of a formal system are Gödel sentences

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#logic #axioms #philosophy #incompleteness #higher-order-logic
146
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Annihilator Method. Getting wrong answer

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#ordinary-differential-equations #higher-order-logic
141
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(How) do theories of higher-order arithmetic have non-$\beta$ models?

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#logic #higher-order-logic

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