I've never heard the term "finiteness" applied to an algorithm, but I think that's because the definition of an algorithm includes that it must be finite. So think of any algorithm and there is your example of finiteness.

The finiteness Theorem, Axiomatization of Geometry, The 23 problems, formalism, functional analysis, physics, and the number theory are is biggest accomplishments.

1. Finiteness

2. Definiteness

3.

Toma Albu has written:

'Relative finiteness in module theory' -- subject(s): Modules (Algebra)

'Modules sur les anneaux de Krull' -- subject(s): Krull rings, Modules (Algebra), Torsion theory (Algebra)

'Cogalois Theory (Pure and Applied Mathematics)'

Characteristics of algorithms are:

Finiteness: terminates after a finite number of steps

Definiteness: rigorously and unambiguously specified

Input: valid inputs are clearly specified

Output: can be proved to produce the correct output given a valid input

Effectiveness: steps are sufficiently simple and basic.