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Principle of Proof by Induction on a Well-ordering

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#elementary-set-theory #transfinite-recursion
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Do we know if there exist true mathematical statements that can not be proven?

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#logic #induction #proof-theory #transfinite-recursion
869
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Transfinite recursion and Replacement

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#set-theory #transfinite-recursion
498
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Initial Segment Order Isomorphic to the Ordinal Numbers

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#set-theory #proof-writing #ordinals #transfinite-recursion
420
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Translation invariance of sets implies translation invariance of their generated sigma algebra?

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#measure-theory #transfinite-recursion
40
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What should be the number of functions with this condition.

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#functions #transfinite-recursion
312
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"Quantifying" over properties and "operations" in ZFC and transfinite recursion: clarifying confusion

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#set-theory #first-order-logic #foundations #transfinite-recursion
421
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Is Rudy Rucker's Theta (θ) the same as Θ and also the same as the omega-fixed point (the first aleph-fixed point) and the first beth-fixed point?

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#ordinals #transfinite-recursion
1.2k
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Is there a second Church-Kleene ordinal?

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#supremum-and-infimum #ordinals #transfinite-recursion
311
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Is "theory of classes" "constructive" in NBG and ZFC? How to state theorems about "classes" involving $\exists!$?

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#logic #set-theory #first-order-logic #transfinite-recursion
545
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The Ackermann hierarchy vs. the fast growing hierarchy

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#inequality #big-numbers #transfinite-recursion #transfinite-induction #ackermann-function
419
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A slower ordinal collapsing function and the Bachmann-Howard ordinal.

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#set-theory #ordinals #transfinite-recursion
76
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How to find the period of this chaotic map for $x_0=\sqrt{M}$?

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#algebraic-number-theory #conic-sections #continued-fractions #chaos-theory #transfinite-recursion
146
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At what steps is Replacement required in definitions by Transfinite Recursion?

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#elementary-set-theory #transfinite-recursion
105
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How does my modified ordinal hierarchy relate to other ordinal hierachies?

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#approximation #big-numbers #transfinite-recursion

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