A Jech窶適unen tree is a set-theoretic tree with properties that are incompatible with the generalized continuum hypothesis. It is named after Thomas Jech and Kenneth Kunen, both of whom studied the possibility and consequences of its existence.
A マ1-tree is a tree with cardinality and height マ1, where マ1 is the first uncountable ordinal and is the associated cardinal number. A Jech窶適unen tree is a マ1-tree in which the number of branches is greater than and less than .
Thomas Jech ( 1971) found the first model in which this tree exists, and Kenneth Kunen ( 1975) showed that, assuming the continuum hypothesis and , the existence of a Jech窶適unen tree is equivalent to the existence of a compact Hausdorff space with weight and cardinality strictly between and .
A Jech窶適unen tree is a set-theoretic tree with properties that are incompatible with the generalized continuum hypothesis. It is named after Thomas Jech and Kenneth Kunen, both of whom studied the possibility and consequences of its existence.
A マ1-tree is a tree with cardinality and height マ1, where マ1 is the first uncountable ordinal and is the associated cardinal number. A Jech窶適unen tree is a マ1-tree in which the number of branches is greater than and less than .
Thomas Jech ( 1971) found the first model in which this tree exists, and Kenneth Kunen ( 1975) showed that, assuming the continuum hypothesis and , the existence of a Jech窶適unen tree is equivalent to the existence of a compact Hausdorff space with weight and cardinality strictly between and .