isEquiconsistentWith
P28011
predicate
Indicates that two formal theories or systems have the same consistency strength, such that if one is consistent then the other is also consistent, and if one is inconsistent then so is the other.
All labels observed (3)
| Label | Occurrences |
|---|---|
| consistencyQuestion | 1 |
| consistencyRelativeTo | 1 |
| isEquiconsistentWith canonical | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: isEquiconsistentWith
Generated description
Indicates that two formal theories or systems have the same consistency strength, such that if one is consistent then the other is also consistent, and if one is inconsistent then so is the other.
Sample triples (3)
| Subject | Object |
|---|---|
| von Neumann–Bernays–Gödel set theory |
Zermelo–Fraenkel set theory
ⓘ
surface form:
Zermelo–Fraenkel set theory with choice
|
| axiom of choice | Zermelo–Fraenkel set theory if ZF is consistent via predicate surface "consistencyRelativeTo" ⓘ |
| ZF | relative to large cardinal axioms via predicate surface "consistencyQuestion" ⓘ |