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Embedding $^\omega\omega$ and $S_\omega$ with lexicographic order into $\mathbb{R}$

There's a general argument we can use for any question of this form. Cantor's theorem shows that every countable linear order embeds into $\mathbb{Q}$. Consequently, every separable linear order (= ...
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Embedding $^\omega\omega$ and $S_\omega$ with lexicographic order into $\mathbb{R}$

Let $0\leq a_0 < b_0 < a_1 < b_1 < a_2 < b_2 < \ldots \leq 1$, and let $\varphi_k \colon [0,1] \to [a_k,b_k]$ be the unique increasing linear bijection taking $0$ to $a_k$ and $1$ to ...
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Classification of multiplicative lattices

Assuming distributivity, the answer to the first part of Question 1 is simple: Every finite distributive lattice $L$ admits a multiplication, namely the meet operation. Meet is commutative and ...
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