∃x ∀y ¬(y ∈ x)
∀x ∀y ∃z ∀w (w ∈ z ↔ (w = x ∨ w = y))
∀x ∃y ∀z (z ∈ y ↔ ∃w (w ∈ x ∧ z ∈ w))
∀x ∃y ∀z (z ∈ y ↔ ∀w (w ∈ z → w ∈ x))
∃x (∅ ∈ x ∧ ∀y (y ∈ x → (y ∪ {y}) ∈ x))
∀x (x ≠ ∅ → ∀F ∀y ∀z ((∀w (w ∈ x → ∃!u (F(w) = u)) ∧ ∀w (w ∈ x → F(w) = y)) → z ∈ x))
∀x (x ≠ ∅ → ∃y (y ∈ x ∧ y ∩ x = ∅))
0 := ∅
s(x) := x ∪ {x}
∀x (x ≠ ∅ → ∃f (f 是一个选择函数))
0 := ∅
s(x) := x ∪ {x}
1 := s(0) = ∅ ∪ {∅} = {∅}
2 := s(1) = {∅} ∪ {{∅}} = {∅, {∅}}
3 := s(2) = {∅, {∅}} ∪ {{∅, {∅}}} = {∅, {∅}, {{∅, {∅}}}
N = {x | x = 0 ∨ (∃y ∈ N)(x = s(y))}
S ⊆ κ 是稳定的 ⇔ 对于所有闭无界集合C ⊆ κ，S ∩ C ≠ ∅

@混乱无双 @贴吧大艺术家

@影•风 @普鲁尔勒森-西斯

@****1438 @

要用AI的话，建议先把基本集合论和高阶逻辑的书转成pdf喂给他

1 := s(0) = ∅ ∪ {∅} = {∅}
2 := s(1) = {∅} ∪ {{∅}} = {∅, {∅}}
3 := s(2) = {∅, {∅}} ∪ {{∅, {∅}}} = {∅, {∅}, {{∅, {∅}}}
N = {x | x = 0 ∨ (∃y ∈ N)(x = s(y))}
S ⊆ κ 是稳定的 ⇔ 对于所有闭无界集合C ⊆ κ，S ∩ C ≠ ∅
∀P (∀x (P(x) ↔ x = 0 ∨ (∃y (P(y) ∧ x = s(y)))) → ∀x P(x))
∀a ∀b ∃c ∀d (d ∈ c ↔ (d = a ∨ d = b))
∀A ∃B ∀x (x ∈ B ↔ ∃C (C ∈ A ∧ x ∈ C))
∀A ∃P(A) ∀B (B ∈ P(A) ↔ ∀x (x ∈ B → x ∈ A))
∃x (∅ ∈ x ∧ ∀y (y ∈ x → (y ∪ {y}) ∈ x))
∀A (∀x (x ∈ A → ∃!y F(x, y))) → ∃B ∀z (z ∈ B ↔ ∃x (x ∈ A ∧ F(x, z)))
∀x (x ≠ ∅ → ∃y (y ∈ x ∧ y ∩ x = ∅))
∀x (x ≠ ∅ → ∃f (f 是一个选择函数))

嚎…嚎厉害