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an algorithm, that, given a transitive relation T, will return the smallest relation R such that the transitive closure of R is T? Is there such a smallest...

not transitive iff ∈ is transitive on A. Example 1: A={0,{0},{{0}}} is a transitive set, but ∈ is not transitive on A. Example 2: ∈ is transitive on A={{0}}...

S is the transitive closure): If S is antisymmetric, then the reduction is unique, if it exists. If S is locally finite then the transitive reduction...

transitive closure, and remove orientation." Why do I need to apply transitive closure, I though the partial order over the set is already transitive...

...a set is called hereditarily countable if and only if its transitive closure is a countable set. If the axiom of countable choice holds, then a set...

isomorphism between (ω,E) and (X, ∈ {\displaystyle \in } ) where X is the transitive closure of {x}. with this In set theory a code of a set is defined as follows...

transitive closure" (meanwhile?) refers to the very same article it starts from; it should be adjusted or deleted. Similar for "reflexive transitive symmetric...

and to reinforce the message that DAGs are conceptually powerful. Transitive closure is another case where a diagram might do all those things: the Hasse...

my attempt to describe how it finds needed components to achieve transitive closure without being inaccurate or excessively complicated? RJFJR (talk)...

satisfies φ(y) (i.e. with quantifiers restricted to A) for every y in the transitive closure of {x} (which is a subset of A). If B=A, then we are done. Otherwise...

definition given (which is more common in social choice) is similar to transitive closure in reverse. I'll try to explain this better when I think of a way...

theories is to define that A is a hereditary xxx iff every object in the transitive closure of {A} is a xxx (note that this is equivalent to the inductive definition...

the existential quantifier in the right place? Doesn't non-transitive mean "not transitive"? Do you have a reference? --Sam Staton 13:08, 28 August 2007...

(If memory serves, they dealt on the 'value webs' that are the transitive closures of ud- and du-chains, which is the same information as managed in...

comes to mind when given a general reduction relation is its transitive reflexive closure, but the “diamond property” for this preorder amounts to confluence...

meant by "extending by transitivity"? Does it mean transitive closure? Do we also have to do some kind of "symmetric closure" to make this relation symmetric...

are sufficient to recover the original by reachability extension (transitive closure). It is more natural to draw them this way, and cycles are much clearer...

sentence explaining that the term R-ancestor is derived from taking the transitive closure of the parent relation as an example, but gave up when I could not...

not considering that Hasse diagrams are understood to denote the transitive closure of what they actually depict, so I thought the strict-part requirement...

properties of the elements should be as similar as possible (their transitive closures should have a similar structure as graphs); perhaps, we should eliminate...