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