Tarski’s fixed point theorem
E353628
Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Knaster–Tarski theorem | 2 |
| Tarski’s fixed point theorem canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T3380931 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Tarski’s fixed point theorem Context triple: [Alfred Tarski, knownFor, Tarski’s fixed point theorem]
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A.
Kakutani fixed-point theorem
The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
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B.
Glicksberg fixed-point theorem
The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
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C.
Brouwer fixed-point theorem
The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
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D.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
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E.
Kripke fixed-point theory of truth
The Kripke fixed-point theory of truth is a semantic framework developed by Saul Kripke that uses partial truth predicates and fixed points to consistently handle self-referential sentences and semantic paradoxes like the liar paradox.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Tarski’s fixed point theorem Target entity description: Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
-
A.
Kakutani fixed-point theorem
The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
-
B.
Glicksberg fixed-point theorem
The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
-
C.
Brouwer fixed-point theorem
The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
-
D.
Ky Fan’s lemma
Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
-
E.
Kripke fixed-point theory of truth
The Kripke fixed-point theory of truth is a semantic framework developed by Saul Kripke that uses partial truth predicates and fixed points to consistently handle self-referential sentences and semantic paradoxes like the liar paradox.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in lattice theory ⓘ result in order theory ⓘ |
| appliesTo |
isotone maps on complete lattices
ⓘ
monotone endofunctions on complete lattices ⓘ |
| assumptionOnFunction | monotone ⓘ |
| characterizes | set of fixed points as complete lattice ⓘ |
| domain | complete lattice ⓘ |
| field |
denotational semantics
ⓘ
economics ⓘ fixed-point theory ⓘ game theory ⓘ lattice theory ⓘ mathematical logic ⓘ order theory ⓘ program verification ⓘ theoretical computer science ⓘ |
| generalizes | fixed-point results for monotone operators on power sets ⓘ |
| guarantees |
existence of fixed points
ⓘ
existence of greatest fixed point ⓘ existence of least fixed point ⓘ |
| historicalPeriod | 20th century mathematics ⓘ |
| implies | fixed points can be obtained as limits of approximation sequences in complete lattices ⓘ |
| namedAfter | Alfred Tarski ⓘ |
| relatedTo |
Banach fixed-point theorem
ⓘ
Brouwer fixed-point theorem ⓘ Kleene fixed-point theorem ⓘ
linked to:
Kleene’s recursion theorem
Knaster–Tarski theorem ⓘ
linked to:
Tarski’s fixed point theorem
|
| requires |
existence of arbitrary joins
ⓘ
existence of arbitrary meets ⓘ |
| statedIn | order-theoretic terms ⓘ |
| typicalDomainExample |
lattice of subsets ordered by inclusion
ⓘ
powerset lattice of a set ⓘ |
| usedIn |
abstract interpretation
ⓘ
construction of coinductive definitions ⓘ construction of inductive definitions ⓘ dataflow analysis ⓘ definition of semantics of recursive programs ⓘ denotational semantics of programming languages ⓘ economic models of strategic complementarities ⓘ fixed-point logics ⓘ formal verification ⓘ game-theoretic models with monotone best responses ⓘ general equilibrium theory under monotonicity assumptions ⓘ model theory ⓘ proof theory ⓘ μ-calculus semantics ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Tarski’s fixed point theorem Description of subject: Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Tarski’s fixed point theorem
linked to: Tarski’s fixed point theorem
subject linked to:
Alfred Teitelbaum