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how many linear orderings on $\omega$ the are and how can we identify when 2 of them are in fact isomorphic.
how many linear orderings on $\omega$ the are and how can we identify when 2 of them are in fact isomorphic. I think that by instability argument there are $2^{\aleph_0}$ of them, but I do not know ...
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Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
How can I attack this problem?
My idea is for $X \subset \mathbb{N}$ set up a linear order $O_{X}$ such that if $X \not =Y$ then $O_X \not = O_Y$.
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Construction of uncountably many non-isomorphic linear (total) orderings of natural numbers
I would like to find a way to construct uncountably many non-isomorphic linear (total) orderings of natural numbers (as stated in the title).
I've already constructed two non-isomorphic total ...
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