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Higher-Order Logic in ordinary Mathematics?

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#logic #soft-question #philosophy #higher-order-logic
207
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A course on Logic.

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#reference-request #logic #propositional-calculus #first-order-logic #higher-order-logic
55
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Extensionality of a hierarchy of functionals over $\mathbb{N}$

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#lambda-calculus #type-theory #higher-order-logic
186
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Can monadic second-order logic characterize finiteness?

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#logic #higher-order-logic
869
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Formulating that the universe is finite without establishing an upper limit

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#logic #first-order-logic #higher-order-logic
377
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$\exists x ~ \forall y ~ f(x, y) \iff \forall y() ~ \exists x~ f(x, y(x))$ Name? Proof?

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#logic #axioms #higher-order-logic
467
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Expressive Power of Second-Order Logic vs. Higher-Order Logics

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#logic #higher-order-logic
264
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Can the transfer principle apply to second-order logic if we transfer sets and relations to hyper-sets and hyper-relations?

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#logic #nonstandard-analysis #higher-order-logic #nonstandard-models
496
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Is mathematical induction the only known example of a higher-order logic?

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#logic #propositional-calculus #first-order-logic #higher-order-logic
1.3k
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Show that well-ordering is not a first-order property.

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#proof-writing #compactness #first-order-logic #proof-explanation #higher-order-logic
401
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The monadic second order theory with $<$ and Presburger arithmetic

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#logic #foundations #formal-systems #higher-order-logic
1.6k
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What's a good introduction to Second Order Logic

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#logic #book-recommendation #higher-order-logic
774
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Monadic second order logic without constants, functions and equality

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#logic #higher-order-logic
571
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Is the expressive power of infinitary logic language $L(\infty,\infty)$ larger, the same or smaller than that of ZFC+large cardinal axioms?

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#logic #set-theory #cardinals #large-cardinals #higher-order-logic
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Is second order logic even a logic?

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#logic #higher-order-logic

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