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Ideas of Kenneth Kunen, by Text

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

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