- arity, i.e. if it has a
finite number of
input values. Similarly, an
infinitary operation is one with an
infinite number of
input values. In standard...
- An
infinitary logic is a
logic that
allows infinitely long
statements and/or
infinitely long proofs. The
concept was
introduced by
Zermelo in the 1930s...
- In mathematics,
infinitary combinatorics, or
combinatorial set theory, is an
extension of
ideas in
combinatorics to
infinite sets. Some of the
things studied...
- the fact that if a
cardinal is
weakly compact then a
certain related infinitary language satisfies a
version of the
compactness theorem; see below. The...
-
arithmetic combinatorics is the
ergodic theory of
dynamical systems.
Infinitary combinatorics, or
combinatorial set theory, is an
extension of
ideas in...
- 2 {\displaystyle L_{\kappa }^{2}} be the
infinitary logic for second-order set theory,
permitting infinitary conjunctions and
disjunctions of
length <...
- the
context is clear). It is also
possible to
generalize the
concept to
infinitary relations with
infinite sequences. When two objects, qualities, classes...
-
numbers as its domain. Many
extensions of first-order logic,
including infinitary logics and higher-order logics, are more
expressive in the
sense that...
-
notation Knuth's up-arrow
notation Arrow notation (Ramsey theory), or
infinitary combinatorics Arrow notation as a way of
representing functions This disambiguation...
- In
mathematical logic,
geometric logic is an
infinitary generalisation of
coherent logic, a
restriction of first-order
logic due to
Skolem that is proof-theoretically...
