- Mirsky's
theorem the
minimum number of
antichains into
which the set can be partitioned. The
family of all
antichains in a
finite partially ordered set can...
-
common lower bound. Thus
lattices have only
trivial strong antichains (i.e.,
strong antichains of
cardinality at most 1). Kunen,
Kenneth (1980), Set Theory:...
- have
equal values of N, is an
antichain, and
these antichains partition the
partial order into a
number of
antichains equal to the size of the largest...
-
satisfy the
countable chain condition, or to be ccc, if
every strong antichain in X is countable.
There are
really two conditions: the
upwards and downwards...
-
monotone Boolean functions of n variables. Equivalently, it is the
number of
antichains of
subsets of an n-element set, the
number of
elements in a free distributive...
- have
equal values of N, is an
antichain, and
these antichains partition the
partial order into a
number of
antichains equal to the size of the largest...
-
theorem implies the
statement that
there can be no
infinite antichains,
because an
infinite antichain is a set that does not
contain any pair
related by the...
- then the
subsets with
equal labels form a
partition into
antichains, with the
number of
antichains equal to the size of the
largest chain overall. Every...
- with the
maximal antichains in Q: the
elements in the
lower set of a cut
correspond to the
elements with
subscript 0 in an
antichain, and the elements...
- not an
antichain. In
other words, Fin ( E , 2 ) {\displaystyle \operatorname {Fin} (E,2)} -
antichains are countable. The
importance of
antichains in forcing...
