unconditionally impossible. We conclude that the subcountability axiom, asserting all sets are subcountable, is incompatible with P N {\displaystyle {\mathcal...

axiom of powerset is not adopted, in a constructive framework even the subcountability of all sets is then consistent. That all said, in common set theories...

Markovian school is the permitted subcountability of various uncountable collections. When adopting the subcountability of the collection of all unending...

countably many Turing machines, showing that the computable numbers are subcountable. The set S {\displaystyle S} of these Gödel numbers, however, is not...

{\displaystyle \leq } on corresponding cardinals. Homological algebra Subcountable Griess, Robert L. (1982), "The Friendly Giant", Inventiones Mathematicae...

{Q} }^{\mathbb {N} }} or some models of the reals can be taken to be subcountable. That said, Cantors diagonal construction proving uncountability of powersets...