Computability theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
At a glance
Key signals
0% cross fields · reaches 3 more
- Computer Science
- Logic
- Explanation
- Examples
- Misconception
- Sourced relations 2
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
Foundations · builds on
Computability theorydepends onTuring machineEstablished
computability theory depends on Turing machine.
Mechanism: Computability theory rests on the Turing machine: this simple abstract computer defines the very limit of what any algorithm can compute.
- Wikipedia (English & German editions) verifiedmoderate evidence
System context
Computational complexity theoryis aComputability theoryEstablished
Open Computational complexity theory →
computational complexity theory is a kind of computability theory.
Mechanism: Complexity theory refines computability theory: it asks not just whether a problem can be solved, but how much time and space it takes.
- Wikidata verifiedmoderate evidence
Decidabilityis part ofComputability theoryEstablished
Decidability is a computability question.
Mechanism: It asks whether an algorithm can always answer a problem correctly and halt; some problems provably cannot.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Currently dark in the atlas: no key date stored · 3 of 3 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).
structural · Structural graph analysis — not a claim of importance, causation or history.
Structural neighbourhood: 3 → 17 → 49 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
All 3 of its relationships stay within its own discipline — a field-specific concept in the current atlas.
structural · Structural graph analysis — not a claim of importance, causation or history.
cross-field
3 within-field, 0 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
- No dated history stored — the atlas records no key date for this concept. atlas representation
Conditions
- Its dependency reading rests on 1 foundation relation. structural
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Dependency radial
What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Turing machine, Computational complexity theory and Decidability.
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
- Connects 3 other ideas across 2 disciplines.
- A cross-disciplinary bridge — its connections reach into 3 other fields.
- Most of its connections are of the “Kind & structure” kind.
Derived from the graph’s real structure — observations, not a score.
Sources
- Wikipedia (English & German editions) verifiedmoderate evidence
- Wikidata verifiedmoderate evidence