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15
94
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How can initial segment of the set of all natural numbers is equal to itself

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#set-theory #ordinals
139
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Does the number $\frac{1}{\omega}$ exist?

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#real-numbers #rational-numbers #ordinals
143
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On the proof that the successor of an ordinal is also an ordinal

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#set-theory #ordinals
67
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A couple of well ordering proofs.

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#set-theory #ordinals #well-orders
104
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Can $ZF$ construct this function?

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#set-theory #axiom-of-choice #ordinals #constructive-mathematics
123
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When we speak of ordinal, do we always refer to natural numbers and theirs successors?

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#set-theory #ordinals
74
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How axiom of substitution implies unique function for ordinals in Halmos book?

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#set-theory #ordinals
134
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Dubious proof in Halmos's book: Two similar ordinal numbers are always equal

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#elementary-set-theory #solution-verification #ordinals
64
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The range of any continuous function from $[0, \omega_1] \times [0, \omega_1] \rightarrow \mathbb{R}$ is countable

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#general-topology #ordinals
96
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Help with basic ordinal arithmetic: What is the supremum of the sequence $\omega^{2} + \omega$, $\omega^{2}*2 + \omega$, $\omega^{2}*3 + \omega$, ...?

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#set-theory #ordinals #transfinite-recursion
38
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The set of predecessors of a node in a tree is finite?

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#relations #order-theory #trees #ordinals
93
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Well ordered set similar to an ordinal is an ordinal?

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#set-theory #ordinals
73
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Is there a model of KP with no $\emptyset'$ ordinal notation for the Bachmann-Howard ordinal?

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#logic #set-theory #ordinals #ordinal-analysis
118
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a proof idea: Every well-ordered set has an order-preserving bijection to exactly one ordinal.

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#logic #solution-verification #set-theory #ordinals #well-orders
88
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Ordinal Arithmetic: $\omega\cdot \omega^{\omega}=\omega^{\omega}$

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#ordinals

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