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Fast-growing hierarchy: Definition, Points of interest & Functions in fast-growing hierarchies

In computability theory, computational complexity theory and proof theory, a fast-growing hierarchy (also called an extended Grzegorczyk hierarchy, or a Schwichtenberg–Wainer hierarchy) is an ordinal-indexed family of rapidly increasing functions fα: N → N (where N is the set of natural numbers {0, 1, ...}, and α ranges up to some large countable…

Language: English [EN]
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Fast-growing hierarchy topic overview

The analysis highlights Definition, Points of interest and Functions in fast-growing hierarchies as prominent areas in the source structure around Fast-growing hierarchy.

Related topics
32
Source areas
5
Connected nodes
37
Extracted relationships
20
Related term clusters
29
Bridge connections
37

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Definition · 11 topics
Overview · 8 topics
Points of interest · 8 topics
Functions in fast-growing hierarchies · 3 topics
The Wainer hierarchy · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

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Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definition

The Wainer hierarchy

Points of interest

Functions in fast-growing hierarchies

For the semantics nerds

You can skip this section if you’re here for content ideas and keyword inspiration.

Advanced semantic analysis

How Fast-growing hierarchy connects Entity context

The extracted context around Fast-growing hierarchy shows recurring relationship patterns in the source. For example, Fast-growing hierarchy → Ackermann, Bachmann, Every, Following, Friedman's TREE, Furthermore, Grzegorczyk, Hardy, Hence, Howard, ID, Peano, Peano Arithmetic, The Goodstein, The Hardy, The Wainer, Wainer Another extracted example is Fast-growing hierarchy → Cantor, The Wainer. Use these groups to spot repeated connection types before inspecting the individual relationships.

Fast-growing hierarchy

Top relations

related to Points of interest · 17
Fast-growing hierarchy → Ackermann, Bachmann, Every, Following, Friedman's TREE, Furthermore, Grzegorczyk, Hardy, Hence, Howard, ID, Peano, Peano Arithmetic, The Goodstein, The Hardy, The Wainer, Wainer
related to The Wainer hierarchy · 2
Fast-growing hierarchy → Cantor, The Wainer
related to Functions in fast-growing hierarchies · 1
Fast-growing hierarchy → Grzegorczyk

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

hierarchy wainer ε0 functions fα function ordinal fast-growing every computable fundamental total grzegorczyk definition limit fε0 natural iterate sequences beyond

Fast-growing hierarchy relationships Subject–Predicate–Object triples

TTTA extracted 20 structured relationships around Fast-growing hierarchy. Examples in this analysis include Fast-growing hierarchy → related to Functions in fast-growing hierarchies → Grzegorczyk and Fast-growing hierarchy → related to Points of interest → Following. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Fast-growing hierarchyrelated to Functions in fast-growing hierarchiesGrzegorczyk0.60section
Fast-growing hierarchyrelated to Points of interestFollowing0.60section
Fast-growing hierarchyrelated to Points of interestEvery0.60section
Fast-growing hierarchyrelated to Points of interestWainer0.60section
Fast-growing hierarchyrelated to Points of interestBachmann0.60section
Fast-growing hierarchyrelated to Points of interestGrzegorczyk0.60section
Fast-growing hierarchyrelated to Points of interestHence0.60section
Fast-growing hierarchyrelated to Points of interestAckermann0.60section
Fast-growing hierarchyrelated to Points of interestPeano0.60section
Fast-growing hierarchyrelated to Points of interestThe Goodstein0.60section
Fast-growing hierarchyrelated to Points of interestPeano Arithmetic0.60section
Fast-growing hierarchyrelated to Points of interestFriedman's TREE0.60section

Related concept clusters Related term clusters

The concept neighborhoods around Fast-growing hierarchy bring nearby vocabulary together. In this analysis, examples include Ε0, Fα and Functions. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Fast-growing hierarchy
    • Ε0
    • Fα
    • Functions
    • Ordinal
    • Large
    • Hierarchy
    • Limit
    • Grzegorczyk
    • Fundamental
    • Fε0
    • Total
    • Every
  • fast-growing hierarchy
    • Wainer
    • Ε0
    • Function
    • Functions
    • Fα
    • Ordinal
    • Large
    • Every
    • Hierarchy
    • Limit
    • Fundamental
    • Grzegorczyk
  • grzegorczyk hierarchy
    • Wainer
    • Large
    • Ε0
    • Function
    • Functions
    • Fα
    • Every
    • Ordinal
    • Finite
    • Fundamental
    • Iterate
    • Natural
  • computable function
    • Hierarchy
    • Wainer
    • Total
    • Every
    • Fα
    • Dominated
    • Ackermann
    • Fω
    • Arithmetic
    • Iterate
    • Peano
    • Provably
  • large countable ordinal
    • Definition
    • Limit
    • Natural
    • Ordinals
    • See
    • Sequence
    • Fundamental
    • Every
    • Interest
    • Points
    • Finite
    • Growth
  • fundamental sequence (ordinals)
    • Sequences
    • Limit
    • Ordinals
    • See
    • Sequence
    • Finite
    • Beyond
    • Fα
    • Hierarchy
    • Interest
    • Points
    • Wainer
  • iterated function
    • Hierarchy
    • Wainer
    • Fα
    • Dominated
    • Total
    • Ackermann
    • Fω
    • Hence
    • Iterate
    • Ε0
    • Fε0
    • Grzegorczyk
  • buchholz psi function
    • Hierarchy
    • Wainer
    • Fα
    • Dominated
    • Total
    • Ackermann
    • Fω
    • Hence
    • Iterate
    • Ε0
    • Fε0
    • Grzegorczyk

Connections between topic areas Semantic bridges

For Fast-growing hierarchy, one of the stronger structural bridges in this analysis connects Fast-growing hierarchy with Definition. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Fast-growing hierarchy — Definition · splits 26 ⟂ 12
Fast-growing hierarchy — Overview · splits 29 ⟂ 9
Fast-growing hierarchy — Points of interest · splits 29 ⟂ 9
Fast-growing hierarchy — Functions in fast-growing hierarchies · splits 34 ⟂ 4
Fast-growing hierarchy — The Wainer hierarchy · splits 35 ⟂ 3

Map overview Semantic statistics

Fast-growing hierarchy

Nodes38
Edges37
Triples20
Avg. degree1.95
Density0.052632
Components1

Source & methodology

TTTA analyzes the structure around Fast-growing hierarchy to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Definition, Points of interest & Functions in fast-growing hierarchies, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Fast-growing hierarchy · EN edition · Analysis: TopicsToTalkAbout

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