These functions and relations could be Infinitary.
They are finitary representations again of Infinitary objects.
they might be Infinitary.
their effects could be Infinitary. The moment you are trying to.
Some mathematical function or relation. These functions and relations could be Infinitary.
anything that is Infinitary is not part of the computational process with some restrictions.
Here is a case of our finitary specification as opposed to this Infinitary specification.
You have rules of inferential logic which are always finitary or they might be Infinitary.
If you look at propositional logic, it does not allow you to specify Infinitary objects.
Objects are finitary but their effects could be Infinitary. The moment you are trying to.
Represent any Infinitary object in a finite manner you require it to be machine understandable
Of this set should satisfy. Here is a case of our finitary specification as opposed to this Infinitary specification.
Like if you have axiom schemas, or rules like modes ponens etc.
They are finitary representations again of Infinitary objects.
Process period. We are interested in those kinds of Infinitary objects which somehow have finitary representations.
It can be infinite sets represented as predicates like unary.
Represent any Infinitary object in a finite manner you require it to be machine understandable
and you also require certain rules. Let us look at this process of essentially.
Binary, and ternary but some finitary sets with a finitary representation.
We are interested in Infinitary computational processes which have finitary representations.
We are interested in programming languages which allow for finitary representation of inherently Infinitary objects.
What kinds of Infinitary objects are we normally concerned with?
In the most general case an algorithm is what you want to represent in a program. An algorithm in the most general case is a function from some domain to some co domain.
Algorithm, to define the notion of the computational process, to be able to exactly define what is possible by a computational process and what is not possible by a computational process. Everything that is possible by a computational process should have a finite representation and
anything that is Infinitary is not part of the computational process with some restrictions.