Teori order: Perbedaan antara revisi

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* [[Complete lattice]]s, where every set has a supremum and infimum, and
* [[Directed complete partial order]]s (dcpos), that guarantee the existence of suprema of all [[directed set|directed subsets]] and that are studied in [[domain theory]].
* [[Partial orders with complements]], or ''poc sets'',<ref>Martin A. Roller. Poc sets, median algebras and group actions. An extended study of Dunwoody's construction and Sageev's theorem. preprint, 1998.</ref> are posets ''S'' having a unique bottom element ''0∈S'', along with an order-reversing involution, such that <math>a\leq a^{*} \Rightarrow a=0</math>.
 
However, one can go even further: if all finite non-empty infima exist, then ∧ can be viewed as a total binary operation in the sense of [[universal algebra]]. Hence, in a lattice, two operations ∧ and ∨ are available, and one can define new properties by giving identities, such as
* [http://www.apronus.com/provenmath/orders.htm Orders at ProvenMath] partial order, linear order, well order, initial segment; formal definitions and proofs within the axioms of set theory.
* Nagel, Felix (2013). [http://www.felixnagel.org Set Theory and Topology. An Introduction to the Foundations of Analysis]
 
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