Definitions
from The Century Dictionary.
 Pertaining to infinite quantity.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics, logic Of or pertaining to expressions of
infinite length
Etymologies
Sorry, no etymologies found.
Examples

The former created in 1951 an infinitary sequent calculus to present consistency proofs in a perspicuous way, the latter instead used a more traditional Gentzenstyle calculus.

On the other hand, the consistency of an atomistic theory is typically guaranteed by the trivial oneelement model (with ˜P™ interpreted as identity), though we can also have models of atomistic theories that allow for infinitary decomposition.

The theorem fails badly for nearly all infinitary languages.

For there is a sense in which (P. 16Ï) might tought to be redundant in the presence of infinitary sum principles such as (P. 15Ï) and the like.

(It appears, in an infinitary form, as Mackey's axiom V; a related but stronger condition appears in the definition of a partial Boolean algebra in the work of Kochen and Specker [1965].)

The algebraic strength of GEM, and of its weaker finitary and infinitary variants, is worth emphasizing, but it also reflects substantive mereological postulates whose philosophical underpinnings leave room for controversy.

There are similar but more complicated theorems for uncountable firstorder languages; some of these can be paraphrased as omitting types theorems for infinitary languages.

We can get even stronger composition principles by considering infinitary bounds and sums.

Thus, intuitively, each of the infinitary sum principles above should have a substitution instance that yields

An initial and rough answer to this last question is contained in our discussion so far: Dedekind's approach is settheoretic and infinitary, while Kronecker's is constructivist and finitary.
Comments
Log in or sign up to get involved in the conversation. It's quick and easy.