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Honest leftmost branch

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Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionDec 22, 2024
Entity authorityQ5893284 ↗
Source-derived summary

In set theory, an honest leftmost branch of a tree T on ω × γ is a branch (maximal chain) ƒ ∈ [T] such that for each branch g ∈ [T], one has ∀ n ∈ ω : ƒ(n) ≤ g(n). Here, [T] denotes the set of branches of maximal length of T, ω is the smallest infinite ordinal (represented by the natural numbers N), and γ is some other ordinal.

See also

Scale (computing)

Suslin set

References

Akihiro Kanamori, The Higher Infinite, Perspectives in Mathematical Logic, Springer, Berlin, 1997.

Yiannis N. Moschovakis, Descriptive set theory, North-Holland, Amsterdam, 1980.

Editorial summary

This brief starts where responsible research should: with the source description of “Honest leftmost branch” as open-knowledge reference entry. Everything that follows is an evidence route, not borrowed authority.

Editorial reviewA practical starting point whose main value is the path it opens into stronger specialist and primary sources. The current lead gives the account dated anchors—1997, 1980—that can be checked directly. The selected authority fields contribute no independent date. The account is most persuasive where Honest, leftmost and branch can be independently traced.
Editorial analysis

Why this record matters

The subject matters to the general reference register because the source frames it as open-knowledge reference entry. Its deeper value depends on whether names, dates, institutions and citations support that framing.

Evidence profile

Vocabulary and entity names are the principal evidence signals here, because they determine the precision of every later search. The source revision retrieved here is dated Dec 22, 2024. The linked authority identifier is Q5893284. None of the 0 selected statements returned an explicit reference. The first chronological checks are 1997 and 1980.

Critical limits

The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.

How to read it

Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.

Best used for
  • Subject orientation
  • Search vocabulary
  • Locating named sources
Verify next

The closest primary source, responsible institution and strongest cited specialist reference.

Three-step research path

  1. Establish the record: confirm the title “Honest leftmost branch”, its source revision and the description used here.
  2. Expand the search: follow Honest leftmost branch primary sources, Honest leftmost branch archive and Honest research across catalogues and specialist indexes.
  3. Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.

Questions for further research

  1. Which source most directly establishes the central claim about “Honest leftmost branch”?
  2. Which institution is responsible for the underlying evidence?
  3. Which cited source is closest to the event, object or claim?
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Source & attribution

This entry incorporates text from “Honest leftmost branch” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.