…无论是始终承认它还是否定它，都绊倒过不少世界级的数学家！我目前读了大概三分之一这本追溯其发展历程的极有趣的历史书，G.H. Moore 写的《Zermelo's Axiom of Choice》（2013年）：http://www.amazon.com/gp/product/0486488411/ref=as_li_tl?ie=... (目录：http://www.apronus.com/math/zermelos.htm)
…that consistently affirming or denying it has tripped up many world-class mathematicians! I am currently about 1/3 of the way through this really interesting history that tries to trace that development, Zermelo's Axiom of Choice by G.H. Moore (2013): http://www.amazon.com/gp/product/0486488411/ref=as_li_tl?ie=... (ToC: http://www.apronus.com/math/zermelos.htm)
…HoTT 书的第 3 章）。在这种设定下，选择公理表示对于任意集合 X，(∀ (x : X). ∥ P x ∥) → ∥ ∀ (x : X). P x ∥（见 3.8 节）。注意，从同伦类型论（homotopy type theory）的角度来看，Zermelo 的选择公理太强了：它等价于全局选择公理（global choice，对所有类型 A，∥ A ∥ → A），这与单价公理（univalence）是不相容的。
…3 of the HoTT book). In this setting the axiom of choice says that for any set X, (∀ (x : X). ∥ P x ∥) → ∥ ∀ (x : X). P x ∥ (see section 3.8). Note that from the perspective of homotopy type theory, Zermelo's axiom of choice is too strong: it is equivalent to global choice (for all types A, ∥ A ∥ → A), which is inconsistent with univalence.
…无论是始终承认它还是否定它，都绊倒过不少世界级的数学家！我目前读了大概三分之一这本追溯其发展历程的极有趣的历史书，G.H. Moore 写的《Zermelo's Axiom of Choice》（2013年）：http://www.amazon.com/gp/product/0486488411/ref=as_li_tl?ie=... (目录：http://www.apronus.com/math/zermelos.htm)
…that consistently affirming or denying it has tripped up many world-class mathematicians! I am currently about 1/3 of the way through this really interesting history that tries to trace that development, Zermelo's Axiom of Choice by G.H. Moore (2013): http://www.amazon.com/gp/product/0486488411/ref=as_li_tl?ie=... (ToC: http://www.apronus.com/math/zermelos.htm)
…HoTT 书的第 3 章）。在这种设定下，选择公理表示对于任意集合 X，(∀ (x : X). ∥ P x ∥) → ∥ ∀ (x : X). P x ∥（见 3.8 节）。注意，从同伦类型论（homotopy type theory）的角度来看，Zermelo 的选择公理太强了：它等价于全局选择公理（global choice，对所有类型 A，∥ A ∥ → A），这与单价公理（univalence）是不相容的。
…3 of the HoTT book). In this setting the axiom of choice says that for any set X, (∀ (x : X). ∥ P x ∥) → ∥ ∀ (x : X). P x ∥ (see section 3.8). Note that from the perspective of homotopy type theory, Zermelo's axiom of choice is too strong: it is equivalent to global choice (for all types A, ∥ A ∥ → A), which is inconsistent with univalence.