A NEW DISCOURSE ON UNDECIDEABILITY AND PROOF SYSTEMS.

Abstract

4 In order to better see how one can build a rep around RU, is by taking note of the type of groupings possible of ∩pos. For instance, take note of the number of ones along the columns of the above matrix, we can easily know what progression in number will appear along the columns (as these are inductive in nature) . A blueprint now exists of the number of ones that will appear along such columns starting from any one Bi, this enables us to 'know' what types of numbers are possible of Bn i , in terms of ΣCi thus enabling us to know this finally in terms of the representation : Σ2p-Rep. Note importantly that Bn i will have utmost i in Ci overlapping positions. These along with overlapping positions of ΣBn i can be represented. Since the matrix is always of the same structure regardless of size and is additionally finite in nature, we can always 'know' the progression (what is possible of) of RU thus making it repable. This exact same technique is possible of ∩pos(Ci) as these are also predictably knowable. Predictably knowability of one thing implies PK of the same thing in a different representation. 5A representation can be built, relating RU and pos which can express what is required of pos for RU to be a certain expression or a set of predictable expressions of RU associated to a predictable set of pos-conditions which can be compared to the predictable knowable set of pos(S). Note further that from the nature of the formations of overlapping of one positions being knowable themselves, and also being of some specific mechanical form (because the structure of the expression associated with how these arise being consistent), the progression of RU is informative predictably and can thus be represented, giving more reason for the previous statement. Once RU is predictably represented, we can state conditions required by the mechanistic structure of (which we have shown to exist; as these will be given in terms of pos as pos is related to RU directly) PK(Rep(RU