About: Friedman's finite ordered tree problem   Sponge Permalink

An Entity of Type : owl:Thing, within Data Space : 134.155.108.49:8890 associated with source dataset(s)

The finite ordered tree problem was researched by Harvey Friedman. Friedman defines an ordered tree as a triple (V,≤,<') where (V,≤) is a finite poset with a least element (root) in which the set of predecessors under ≤ of each vertex is linearly ordered by ≤, and where for each vertex, <' is a strict linear ordering on its immediate successors. He also defines the following: * Vertex x ≤* y iff x is to the left of y, or if x ≤ y. * d(v) is the position of v in counting from 1. * |T[0]| = 1 * |T[1]| = 2 * |T[2]| = 4 * |T[3]| = 14 * |T[4]| > 243 * |T[5]| > 2↑↑2295

AttributesValues
rdfs:label
  • Friedman's finite ordered tree problem
rdfs:comment
  • The finite ordered tree problem was researched by Harvey Friedman. Friedman defines an ordered tree as a triple (V,≤,<') where (V,≤) is a finite poset with a least element (root) in which the set of predecessors under ≤ of each vertex is linearly ordered by ≤, and where for each vertex, <' is a strict linear ordering on its immediate successors. He also defines the following: * Vertex x ≤* y iff x is to the left of y, or if x ≤ y. * d(v) is the position of v in counting from 1. * |T[0]| = 1 * |T[1]| = 2 * |T[2]| = 4 * |T[3]| = 14 * |T[4]| > 243 * |T[5]| > 2↑↑2295
dcterms:subject
dbkwik:googology/p...iPageUsesTemplate
abstract
  • The finite ordered tree problem was researched by Harvey Friedman. Friedman defines an ordered tree as a triple (V,≤,<') where (V,≤) is a finite poset with a least element (root) in which the set of predecessors under ≤ of each vertex is linearly ordered by ≤, and where for each vertex, <' is a strict linear ordering on its immediate successors. He also defines the following: * Vertex x ≤* y iff x is to the left of y, or if x ≤ y. * d(v) is the position of v in counting from 1. He then defines T[k] to be the tree of height k such that every vertex v of height ≤k - 1 has exactly d(v) children, and |T[k]| to be number of children. Friedman has proven that |T[k]| has a similar growth rate to that of the Ackermann function. The first few values are as follows: * |T[0]| = 1 * |T[1]| = 2 * |T[2]| = 4 * |T[3]| = 14 * |T[4]| > 243 * |T[5]| > 2↑↑2295
Alternative Linked Data Views: ODE     Raw Data in: CXML | CSV | RDF ( N-Triples N3/Turtle JSON XML ) | OData ( Atom JSON ) | Microdata ( JSON HTML) | JSON-LD    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 07.20.3217, on Linux (x86_64-pc-linux-gnu), Standard Edition
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2012 OpenLink Software