Combining Texts
Ideas for
'Through the Looking Glass', 'The Thought: a Logical Enquiry' and 'Set Theory'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
11 ideas
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) [Kunen]
|
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) [Kunen]
|
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) [Kunen]
|
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) [Kunen]
|
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) [Kunen]
|
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) [Kunen]
|
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))) [Kunen]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036
|
Choice: ∀A ∃R (R well-orders A) [Kunen]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029
|
Set Existence: ∃x (x = x) [Kunen]
|
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031
|
Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
|
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) [Kunen]
|