Description
ZFC axioms and foundational definitions. Extensionality (sets equal iff same members); Null Set; Pairing; Power Set; Union; Infinity; Separation (subset formation); Replacement; Foundation (no ∈-chains); Choice. Arrows mean "depends on".
Source: Stanford Encyclopedia of Philosophy; Zermelo (1908), Fraenkel (1922)
Dependency Flowchart
Note: Arrows mean "depends on" (tail → head).
graph TD
A1["A1 Extensionality\nx=y iff same members"]
A2["A2 Null Set\n∃x ∀y y∉x"]
A3["A3 Pairing\n∀x∀y ∃z z=x,y"]
A4["A4 Power Set\n∀x ∃y y=𝒫x"]
A5["A5 Union\n∀x ∃y y=⋃x"]
A6["A6 Infinity\n∃ω inductive set"]
A7["A7 Separation\nsubset by formula"]
A8["A8 Replacement\nimage of set is set"]
A9["A9 Foundation\nno ∈-descending chain"]
A10["A10 Choice\nselector for disjoint family"]
Def1["Def: ∅ unique\nempty set"]
Def2["Def: ⊆\nsubset"]
Def3["Def: ∪ ∩\nunion, intersection"]
T1["Thm: ∅ unique"]
T2["Thm: {a,b} unique"]
A1 --> T1
A2 --> T1
T1 --> Def1
A1 --> Def2
A3 --> T2
A1 --> T2
T2 --> Def3
A5 --> Def3
A7 --> Def3
classDef axiom fill:#ff6b6b,color:#fff,stroke:#c0392b
classDef definition fill:#b197fc,color:#fff,stroke:#9775fa
classDef theorem fill:#51cf66,color:#fff,stroke:#40c057
class A1,A2,A3,A4,A5,A6,A7,A8,A9,A10 axiom
class Def1,Def2,Def3 definition
class T1,T2 theorem
Color Scheme
Red
Axioms
Axioms
Violet
Definitions
Definitions
Green
Theorems
Theorems
Process Statistics
- Nodes: 15
- Edges: 10
- Axioms: 10
- Definitions: 3
- Theorems: 2