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Showing that $\Bbb{N}$ is well-ordered. Do I need an arbitrary case?

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#elementary-set-theory #order-theory #well-orders
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How to prove there exists an uncountable well-ordered set without using axiom of replacement

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#set-theory #well-orders
664
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isomorphism from well ordered set to ordinal

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#set-theory #ordinals #well-orders
141
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Jech Set Theory 3rd Edition Ex 3.10

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#set-theory #well-orders
36
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Prove that $p\le x<p+1$ by well ordering property

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#number-theory #analysis #well-orders
273
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the power set of every well-ordered set is well-ordered implies well ordering

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#axiom-of-choice #well-orders
162
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Example of Set which possesses well ordering property other than Integers

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#real-analysis #number-theory #well-orders
120
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What is the order type of the set of smooth functions ordered by growth rate?

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#real-analysis #general-topology #order-theory #ordinals #well-orders
257
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Prove of function is surjective iff it has a right inverse using the well-ordering Theorem

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#set-theory #well-orders
110
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Is this an equivalent form of the Well-Ordering Principle?

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#elementary-set-theory #order-theory #well-orders
612
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Finding a well-ordering of the natural numbers of a given order type

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#set-theory #order-theory #ordinals #well-orders #transfinite-recursion
419
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Proving well ordering principle from PMI (PCI) from peano axioms

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#proof-verification #proof-explanation #order-theory #peano-axioms #well-orders
58
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Equivalence between conditions for induction on well-ordered sets.

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#induction #order-theory #well-orders
143
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If $\omega^\alpha$ has cofinality $\omega^\beta$, and $\beta\le\gamma\le\alpha$, does it also have a cofinal subset of order type $\omega^\gamma$?

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#set-theory #order-theory #ordinals #well-orders
201
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Given an ordinal with a particular cofinality, can we find other cofinal subsets with order type and cofinality at least that large?

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#set-theory #order-theory #ordinals #well-orders

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