Dana Scott proved that the existence of a certain kind of these things implies that the von Neumann (“NOY-mahn”) universe does not equal the minimal inner model of ZFC. Projective determinacy is implied by the existence of infinitely many of a type of these things introduced by Hugh Woodin (“wood-in”). The inaccessible type of these things are so called because they cannot be reached from below by performing arithmetic on these things. The Cantor–Schrӧder–Bernstein theorem states that if one of these things is both less than and greater than another of these things, then they are the same. This value for any countably infinite set is the same as this value for the natural numbers. There are none of these things between aleph-naught and “two to the aleph-naught” by the continuum hypothesis. For 10 points, name these values that measure a set’s size. ■END■
ANSWER: cardinal numbers [or cardinality or cardinalities; accept specific types of cardinal, such as large cardinals; prompt on sizes of sets until “size” is read]
<Other Science>
= Average correct buzz position