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Results tagged with linear-orders
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user 9550
15
votes
Accepted
Is it possible to reconstruct an order type from its initial segments?
The answer is No.
Let $\eta$ be the order type of $\mathbb{Q}$, and $\omega_1$ - the order type of the set of countable ordinals. The order types $\eta$ and $\eta \cdot \omega_1$ are different (becau …
- 6,819
20
votes
2
answers
1k
views
An order type $\tau$ equal to its power $\tau^n, n>2$
(This is a re-post of my old unanswered question from Math.SE)
For purposes of this question, let's concern ourselves only with linear (but not necessarily well-founded) order types.
Recall that:
…
- 6,819