### Ideas of Kenneth Kunen, by Theme

#### [American, fl. 1980, At the University of Texas, Austin.]

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###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
 13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y)
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
 13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z)
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
 13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A)
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
 13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x)
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
 13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y)
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
 13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y)
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
 13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y)))
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
 13036 Choice: ∀A ∃R (R well-orders A)
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
 13029 Set Existence: ∃x (x = x)
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
 13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ)
###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
 13040 Constructibility: V = L (all sets are constructible)
###### 8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation
 18465 An 'equivalence' relation is one which is reflexive, symmetric and transitive