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Does second-order arithmetic (Z2) prove soundness and uniform reflection for first-order arithmetic (PA)?

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#logic #proof-theory #incompleteness #higher-order-logic
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annihilator method confusion

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#ordinary-differential-equations #higher-order-logic
135
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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
459
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Why aren't there any first-order sentences which have the property of being true in all non-standard models of PA and false in the standard one?

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#first-order-logic #higher-order-logic #nonstandard-models
2.1k
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Types versus kinds and sorts

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#logic #lambda-calculus #type-theory #higher-order-logic
423
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Is it possible to prove that the encoding of existentials in System F is valid?

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#logic #proof-theory #higher-order-logic #constructive-mathematics
222
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Completness in higher order logic and Interpretations

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#logic #model-theory #higher-order-logic
497
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Proving property for all predicates in first order logic

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#logic #first-order-logic #quantifiers #fake-proofs #higher-order-logic
267
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Are higher order logics substantially stronger than second order

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#logic #higher-order-logic
406
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Logic question in Real Analysis

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#real-analysis #limits #logic #predicate-logic #higher-order-logic
230
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What is the difference between logical and iterative set

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#logic #foundations #higher-order-logic
179
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Second order universal quantifier elimination restriction

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#logic #quantifiers #higher-order-logic #natural-deduction
264
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Is the first-order incompleteness of a theory (like arithmetics, set theory or logic itself) avoidable in a second or higher-order axiomatizations?

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#logic #set-theory #philosophy #higher-order-logic
3.3k
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What's an example of a theory that's consistent yet has no model?

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#logic #higher-order-logic
182
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Can "tit for tat" strategy be defined in monadic second-order logic?

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#logic #game-theory #trees #higher-order-logic

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