### Some articles on *poset, posets*:

Ranked

... In mathematics, a ranked partially ordered set - or

**Poset**... In mathematics, a ranked partially ordered set - or

**poset**- may be either a graded**poset**, or a**poset**that has the property that for every element x, all maximal chains among those with x as ... from the first in that it requires all minimal elements to have the same rank for**posets**with a least element, however, the two requirements are equivalent ... The third definition is even more strict in that it excludes**posets**with infinite chains and also requires all maximal elements to have the same rank ...Boolean-valued Model - Relationship To Forcing

... In one form, forcing "adds to the universe" a generic subset of a

... In one form, forcing "adds to the universe" a generic subset of a

**poset**, the**poset**being designed to impose interesting properties on the newly-added object ... The wrinkle is that (for interesting**posets**) it can be proved that there simply is no such generic subset of the**poset**... forcing A forcing relation is defined between elements p of the**poset**and formulas φ of the forcing language ...Locally Finite

... In mathematics, a locally finite

**Poset**... In mathematics, a locally finite

**poset**is a partially ordered set P such that for all x, y ∈ P, the interval consists of finitely many elements ... Given a locally finite**poset**P we can define its incidence algebra ... In theoretical physics a locally finite**poset**is also called a causal set and has been used as a model for spacetime ...Chain Complete - Properties

... Zorn's lemma states that, if a

... Zorn's lemma states that, if a

**poset**has an upper bound for every chain, then it has a maximal element ... Thus, it applies to chain complete**posets**, but is more general in that it allows chains that have upper bounds but do not have least upper bounds ... Chain complete**posets**also obey the Bourbaki–Witt theorem, a fixed point theorem stating that, if f is a function from the**poset**to itself with the property that, for all x, f(x) ≥ x, then f has a fixed point ...Graded

... In mathematics, in the branch of combinatorics, a graded

**Poset**... In mathematics, in the branch of combinatorics, a graded

**poset**, sometimes called a ranked**poset**(but see the article for an alternative meaning), is a partially ordered set (**poset**...Main Site Subjects

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