In mathematics, a Suslin algebra is a
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in e ...
that is
complete
Complete may refer to:
Logic
* Completeness (logic)
* Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable
Mathematics
* The completeness of the real numbers, which implies t ...
,
atomless, countably
distributive, and satisfies the
countable chain condition In order theory, a partially ordered set ''X'' is said to satisfy the countable chain condition, or to be ccc, if every strong antichain in ''X'' is countable.
Overview
There are really two conditions: the ''upwards'' and ''downwards'' countable c ...
. They are named after
Mikhail Yakovlevich Suslin.
The existence of Suslin algebras is independent of the axioms of
ZFC, and is equivalent to the existence of
Suslin trees or
Suslin line In mathematics, Suslin's problem is a question about totally ordered sets posed by and published posthumously.
It has been shown to be independent of the standard axiomatic system of set theory known as ZFC: showed that the statement can neither ...
s.
See also
Andrei Suslin
Andrei Suslin (russian: Андре́й Алекса́ндрович Су́слин, sometimes transliterated Souslin) was a Russian mathematician who contributed to algebraic K-theory and its connections with algebraic geometry. He was a Trustee ...
References
{{algebra-stub
Boolean algebra
Forcing (mathematics)
Independence results