Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The property of being computable by purely mechanical means.
from The Century Dictionary and Cyclopedia
 n. The quality of being computable.
Etymologies
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Examples

The halting problem is a question in computability theory which asks if an algorithm can be found that decides whether a program (a Turning machine) will finish, or run forever, once given a description of such a program and a finite amount of input.

Ada Lovelace, Haskell Curry, and Noam Chomsky all worked heavily on the foundations of computation/computability theory, and algorithmic programming.

Nicolas Bourbaki, who never existed, is named in the BourbakiWitt theorem, used in computability theory and domain theory.

A latenineteenthcentury mathematician would be able to understand the idea of Turing computability and a von Neumann architecture with a few days instruction.

Creating standards like this allows for better innovation and computability.

Not my fields, but I think this discussion could use some input from an expert in information theory and computability.

Not all computer science focuses on the runtimes of algorithms or the nature of computability.

Subsequently, we will discuss the profound consequences that these paradoxes have on a number of different areas: theories of truth, set theory, epistemology, foundations of mathematics, computability.

I also identified some severe computability problems it seems no one else has.
How do evolutionary processes create information?  The Panda's Thumb

It is also important to stress that a few years later (1938) an analog of the diagonalization lemma (the socalled second recursion theorem) was discovered by Kleene and was soon to become a basic tool in the foundations of recursion theory and computability theory.
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