green numbers give full details.     |    back to list of philosophers     |     expand these ideas

### Ideas of Kenneth Kunen, by Text

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

 1980 Set Theory
 §1.10 p.29 13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y)
 §1.5 p.10 13029 Set Existence: ∃x (x = x)
 §1.5 p.10 13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y)
 §1.5 p.11 13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ)
 §1.6 p.12 13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A)
 §1.6 p.12 13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z)
 §1.6 p.12 13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y)
 §1.6 p.15 13036 Choice: ∀A ∃R (R well-orders A)
 §1.7 p.19 13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x)
 §3.4 p.100 13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y)))
 §6.3 p.170 13040 Constructibility: V = L (all sets are constructible)
 2012 The Foundations of Mathematics (2nd ed)
 I.7.1 p.24 18465 An 'equivalence' relation is one which is reflexive, symmetric and transitive