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Defining multiplication on the non-negative hyperreal numbers ala the Tarski/Eudoxus technique

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#logic #soft-question #axioms #second-order-logic
134
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Interpreting monadic theory of reals in the monadic theory of linear order.

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#real-numbers #order-theory #model-theory #second-order-logic
60
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What subsystem of second-order arithmetic proves the weak Godel’s Theorem?

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#logic #peano-axioms #incompleteness #second-order-logic #reverse-math
176
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What axiom system for the rational numbers is categorical?

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#abstract-algebra #logic #model-theory #rational-numbers #second-order-logic
123
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Axiomatisation of the monadic second order theory of finite linear orders.

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#first-order-logic #order-theory #model-theory #automata #second-order-logic
133
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Can it be shown that there exists no finite proof of CH from second-order set theory?

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#logic #set-theory #meta-math #second-order-logic
514
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How do "we" know the incompleteness of second-order logic?

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#logic #first-order-logic #model-theory #incompleteness #second-order-logic
182
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Do unary relations naturally lead to the notion of sets?

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#logic #predicate-logic #second-order-logic
156
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Does the logical system with the "there exist uncountably many"-quantifier satisfy a variant of upwards Löwenheim-Skolem

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#logic #model-theory #foundations #second-order-logic
332
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Why second order logic is more expressive that the first order logic?

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#first-order-logic #second-order-logic
169
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Limitation of Henkin sematics in second order logic

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#compactness #second-order-logic
144
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How can we trust second-order logic?

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#logic #set-theory #model-theory #second-order-logic
693
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How do you turn a proof of a mathematical statement into a zero-knowledge proof?

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#logic #solution-verification #np-complete #second-order-logic
80
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A problem with the Boolos/Burges/Jeffrey proof of incompleteness of second order logic

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#logic #second-order-logic
203
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"$\Sigma_1^1$-Peano arithmetic" - does it pin down $\mathbb{N}$?

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#logic #set-theory #model-theory #nonstandard-models #second-order-logic

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