Homogeneously Suslin set
Encyclopedia
In descriptive set theory
, a set
is said to be homogeneously Suslin if it is the projection of a homogeneous tree. 
is said to be 
-homogeneously Suslin if it is the projection of a 
-homogeneous tree.
If
is a 
set and 
is a measurable cardinal, then 
is 
-homogeneously Suslin. This result is important in the proof that the existence of a measurable cardinal
implies that
sets are determined
.
Descriptive set theory
In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...
, a set
is said to be homogeneously Suslin if it is the projection of a homogeneous tree. is said to be -homogeneously Suslin if it is the projection of a -homogeneous tree.If
is a set and is a measurable cardinal, then is -homogeneously Suslin. This result is important in the proof that the existence of a measurable cardinalMeasurable cardinal
- Measurable :Formally, a measurable cardinal is an uncountable cardinal number κ such that there exists a κ-additive, non-trivial, 0-1-valued measure on the power set of κ...
implies that
sets are determinedDeterminacy
In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.-Games:...
.