Jónsson function

In set theory, a mathematical discipline, an ω-Jónsson function, named for Bjarni Jónsson, for a set of ordinals "x" is a function from $[x]\; ^omega$ to "x" such that for any subset "y" of "x" with the same cardinality as "x", "f" restricted to $[y]\; ^omega$ maps onto "x". Here if "x" is an ordered set and α is an ordinal, $[x]\; ^alpha$ is the set of subsets of "x" of order type α. So in particular $[x]\; ^omega$ is the set of strictly increasing sequences of "x".

harvs|txt|last=Erdős|last2=Hajnal|year=1966 showed that for any ordinal λ there is an ω-Jónsson function for λ.

ee also

*Jónsson algebra

References

*Citation | last1=Erdős | first1=P. | author1-link=Paul Erdos | last2=Hajnal | first2=András | title=On a problem of B. Jónsson | id=MathSciNet | id = 0209161 | year=1966 | journal=Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques | issn=0001-4117 | volume=14 | pages=19–23
*Citation | last1=Kanamori | first1=Akihiro | title=The Higher Infinite : Large Cardinals in Set Theory from Their Beginnings | publisher=Springer-Verlag | location=Berlin, New York | edition=2nd | isbn=978-3-540-00384-7 | year=2003|page=319