Objects are Finitary but their effects could be inFinitary.
The moment you are trying to.
You have rules of inferential logic which are always Finitary or they might be inFinitary.
Which allow you to generate an infinite number of logical sentences. A Finitary nature of.
We might emphasize that this is actually a Finitary specification and these programs themselves as concrete.
Like if you
have axiom schemas, or rules like modes ponens etc. They are Finitary representations again of inFinitary objects.
In all these cases, we should emphasize the fact that this notation
is important because our notation is to give you a Finitary specification of possibly infinite objects.
Does not allow you the freedom to write these dots and there is no such thing.
You have a method of construction of predicates which is always Finitary.
There are also Finitary specifications and something that is absolutely essential is that it is decidable
by an algorithm whether a certain step in the proof of a logical statement.
By abstraction gives you a Finitary specification so that you can represent the set of even numbers through a notation
which consists of braces that consists of a bound variable.
Be Finitary because the domain could be infinite and the co domain could be infinite. We might think of
an algorithm in general as computing either a function or a method for computing.
Then call one sentence X and the other sentence has the pattern X conditional Y then you are able to infer
Y and you cannot have all rules of inferencing logic. They are Finitary.
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.
Valid sentence of the logical language.
An important element of that logical language is that the generation process should be Finitary. There should be only a finite
set of rules and there should be an algorithm which can clearly tell you whether a given sentence is a well formed sentence of the language.