B. Balcar, F. Franek
Abstract
Open-access reader
We present a proof (without any set-theoretical assumptions) that every infinite complete Boolean algebra includes a free subalgebra of the same cardinality. It follows that the set of all ultrafilters on an infinite complete Boolean algebra $B$ has power $2^{|B|}$.
OpenAlex reports 20 citations for this work. Citation counts describe recorded attention and do not establish research quality.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
We present a proof (without any set-theoretical assumptions) that every infinite complete Boolean algebra includes a free subalgebra of the same cardinality. It follows that the set of all ultrafilters on an infinite complete Boolean algebra $B$ has power $2^{|B|}$.
Key concepts: Complete Boolean algebra, Boolean algebras canonically defined, Mathematics, Stone's representation theorem for Boolean algebras, Free Boolean algebra, Two-element Boolean algebra, Subalgebra, Cardinality (data modeling)