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Topic: Transitive
Replies: 4   Last Post: Apr 27, 2014 5:15 AM

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David C. Ullrich

Posts: 3,555
Registered: 12/13/04
Re: Transitive
Posted: Apr 26, 2014 2:24 PM
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On Sat, 26 Apr 2014 02:09:36 -0700, William Elliot <>

>On Sat, 26 Apr 2014, quasi wrote:
>> William Elliot wrote:
>> >If A is a set, T a transitive set and A in T, is A transitive?
>> Not necessarily.
>> Let x be an atom.
>> Let T = {x,{x},{{x}}} and let A = {{x}}.
>> Then T is transitive, and A is in T, but A is not transitive.

>Let x be the empty set. A isn't transitive. If y in A, then
>y = {x} and y isn't a subset of A, because x in y but x not in A.
>So the answer is not always.
>Ordinals are hereditarily transitive.
>Are there other hereditarily transitve sets?

>An hereditarily transitive set is a set for which every element
>is an hereditarily transitive set.

Not quite...

> Is there a formal definition?

Do you have access to the internet?

>An hereditary set is a set for which every element
>is an hereditary set. Is there a formal definition?

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