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Exercise 7.1.6 Introduction to Set Theory by Hrbacek and Jech

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#set-theory #ordinals #well-orders
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Hessenberg sum/natural sum of ordinals definition

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#elementary-set-theory #set-theory #ordinals #well-orders
1.4k
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Shouldn't the Well Ordering Principle apply only to sets with at least two elements?

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#set-theory #well-orders
34
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The arithmetic of first uncountable ordinal number

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#general-topology #well-orders
89
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Order type of N and Q

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#integers #natural-numbers #well-orders
48
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Detemine whether the interval [4,8] is well-ordered. Explain.

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#discrete-mathematics #well-orders
61
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Is it consistent with ZC that a well-order of type $\omega_\omega$ does not exist?

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#set-theory #cardinals #well-orders
76
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Given two well-orders $\langle A,R \rangle$ and $\langle B,S \rangle$, one of the following holds.

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#set-theory #well-orders
64
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Law of Trichotomy for Well-Orderings

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#elementary-set-theory #set-theory #order-theory #well-orders
49
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Is this set uncountable? $A = \{A_n \colon n \in \mathbb{N}\}$ where $A_n$ is the set $\mathbb{N}$ with the number $n$ removed from it

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#elementary-set-theory #well-orders
2.2k
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Explicit well-ordering of $\mathbb Q$

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#elementary-set-theory #well-orders
1k
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Is there any known uncountable set with an explicit well-order?

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#set-theory #well-orders
357
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Partial order and total order

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#proof-writing #relations #order-theory #well-orders
3.1k
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Any Set of Ordinals is Well-Ordered

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#elementary-set-theory #ordinals #well-orders
695
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Well-orderings of $\mathbb R$ without Choice

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#set-theory #cardinals #real-numbers #ordinals #well-orders

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