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+ | =====Dense linear orders===== | ||
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+ | ====Definition==== | ||
+ | A \emph{dense linear order} is a [[Chains]] $\mathbf{D}=\langle D,\le\rangle$ such that | ||
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+ | $\le$ is \emph{dense}: $x<y\Longrightarrow\exists z (x<z$, $z<y)$ | ||
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+ | |||
+ | Remark: | ||
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+ | ==Morphisms== | ||
+ | Let $\mathbf{C}$ and $\mathbf{D}$ be dense linear orders. A morphism from $\mathbf{C}$ to $\mathbf{D}$ is a function $h:C\rightarrow D$ that is a orderpreserving: | ||
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+ | $x\le y\Longrightarrow h(x)\le h(y)$ | ||
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+ | ====Examples==== | ||
+ | Example 1: | ||
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+ | ====Basic results==== | ||
+ | |||
+ | |||
+ | ====Properties==== | ||
+ | ^[[Classtype]] |first-order | | ||
+ | ^[[Quasiequational theory]] | | | ||
+ | ^[[First-order theory]] | | | ||
+ | ^[[Amalgamation property]] | | | ||
+ | ^[[Strong amalgamation property]] | | | ||
+ | ^[[Epimorphisms are surjective]] | | | ||
+ | ====Finite members==== | ||
+ | |||
+ | $\begin{array}{lr} | ||
+ | None | ||
+ | \end{array}$ | ||
+ | |||
+ | ====Subclasses==== | ||
+ | [[Dense linear orders without endpoints]] | ||
+ | |||
+ | ====Superclasses==== | ||
+ | [[Chains]] | ||
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+ | ====References==== | ||
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+ | [(Ln19xx> | ||
+ | )] | ||
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