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For which subsystems T of 2nd order arithmetic is there a model of T + $\neg$Con(T)?

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#logic #peano-axioms #higher-order-logic
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Why aren't valid higher order logic sentences recursively enumerable in full semantics?

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#logic #set-theory #higher-order-logic
220
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Are proofs for many-sorted first order logic shorter than single sorted first order logic?

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#logic #proof-theory #higher-order-logic
304
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Is there a syntax for type quantification in higher order logic?

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#logic #quantifiers #type-theory #higher-order-logic
1.3k
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What does a prime (apostrophe) mean before a predicate?

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#logic #notation #higher-order-logic
108
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What strongly normalizing lambda calculi exist that can be integrated with/as logic?

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#logic #lambda-calculus #type-theory #higher-order-logic
85
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How do we express higher arity predicates and functions in terms of membership?

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#elementary-set-theory #logic #higher-order-logic
630
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Do I really need lambda abstraction for type theory?

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#logic #lambda-calculus #type-theory #higher-order-logic
401
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How high up do kinds go in type theory?

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#lambda-calculus #type-theory #higher-order-logic
356
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Is there any formula of monadic second-order logic that is only satisfied by an infinite set?

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#logic #higher-order-logic
270
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Are categorical second-order axiomatizations of set theory inconsistent due to the axiom of replacement

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#set-theory #higher-order-logic
221
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Is there a 'largest' second-order categorical axiomatization of set theory, extended from ZFC2

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#set-theory #model-theory #higher-order-logic
205
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Axiomatizability in monadic second-order logic

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#model-theory #first-order-logic #axioms #higher-order-logic
184
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Sound deductive systems with biggest set of provable sentences in second-order logic?

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#logic #higher-order-logic
3k
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How to show incompleteness of second order logic?

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#logic #incompleteness #higher-order-logic

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