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Prove that a set R of real numbers is well ordered iff there is no infinite decreasing sequence of numbers in R

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#discrete-mathematics #elementary-set-theory #well-orders
72
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assumption of well-ordering principle

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#abstract-algebra #well-orders
76
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Can order types of well-ordered proper classes be put in one to one correspondence with $V$?

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#logic #set-theory #ordinals #well-orders #second-order-logic
64
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Equation to Specify Lexicographical Ordering?

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#ordinals #well-orders #ordinal-analysis
89
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Why is $\mathbb{N}$ well-ordered?

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#elementary-set-theory #natural-numbers #well-orders
64
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Why is $(\alpha \times \{0\}) \cup (\beta \times \{1\})$ well-ordered?

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#ordinals #well-orders
220
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Is well-ordered Dedekind-finite set finite?

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#set-theory #axiom-of-choice #ordinals #well-orders
86
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Is a total order formed by set membership necessarily a well order?

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#set-theory #order-theory #ordinals #well-orders
250
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Two questions about the first order theory of well ordered sets.

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#model-theory #well-orders
181
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Ordinal addition is associative (prove with well-order definition).

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#set-theory #ordinals #well-orders
38
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$X\subseteq Y \implies Ord(X) \subseteq Ord(Y)$

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#set-theory #ordinals #well-orders
147
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Can a well ordering well order itself?

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#set-theory #arithmetic #first-order-logic #order-theory #well-orders
46
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Similarities between well ordered sets

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#set-theory #well-orders
318
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Question on a step of "A Simple Proof of Zorn's Lemma" by Lewin

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#set-theory #order-theory #axiom-of-choice #well-orders
75
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Every compact chain has a convergent subchain

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#general-topology #metric-spaces #order-theory #lattice-orders #well-orders

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