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How exactly does Halmos define an ordered pair?

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#elementary-set-theory #well-orders
277
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Analyzing the proof of Kirszbraun's theorem

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#analysis #proof-explanation #compactness #lipschitz-functions #well-orders
123
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Meaning of 'set of well-ordered sequences'

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#sequences-and-series #commutative-algebra #modules #well-orders #injective-module
60
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Open sets in $S_\Omega$ (minimal uncountable well ordered set) with the order topology.

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#general-topology #order-theory #well-orders
95
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Infinite Lexicographic Order on Bijections is Well-Order

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#set-theory #order-theory #axiom-of-choice #ordinals #well-orders
85
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Transfinite Recursion Theorem - Particular case - Enderton

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#set-theory #well-orders #transfinite-recursion
51
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Construct the embedding of a subset of a well-order to the full set

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#set-theory #ordinals #well-orders
101
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Order type of a set that is ordered but not well-ordered

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#elementary-set-theory #order-theory #well-orders
88
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Are suborders of pseudo-well-ordered sets themselves pseudo-well-ordered?

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#model-theory #well-orders
125
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Are $\Bbb{R}\times\Bbb{Q}$ and $\Bbb{Q}\times\Bbb{R}$ order-isomorphic?

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#set-theory #order-theory #well-orders
68
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Is there an order-preserving injection from $\alpha\cdot\alpha+\omega$ to $\mathcal{P}(|\alpha|)$?

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#set-theory #order-theory #ordinals #well-orders
169
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CH, countable additivity, and Ulam's Theorem

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#measure-theory #proof-explanation #set-theory #well-orders
129
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Continuation of well ordered sets

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#set-theory #well-orders
75
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Is the identity function the only order-preserving isomorphism between a linearly-ordered set and itself?

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#elementary-set-theory #order-theory #well-orders
36
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Countryman type is a Specker type: an unclear point in the proof

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#elementary-set-theory #order-theory #well-orders

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