Partition theorems and ultrafilters
Partition theorems and ultrafilters
We introduce a class of ultrafilters on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega"> <mml:semantics> <mml:mi>ω<!-- ω --></mml:mi> <mml:annotation encoding="application/x-tex">\omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> called <italic>k</italic>-arrow ultrafilters and characterized by the partition relation <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper U right-arrow left-parenthesis upper U comma k right-parenthesis squared"> <mml:semantics> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo stretchy="false">→<!-- → …