By the Law of the Excluded Middle ( in our classical metatheory ), P must either hold nowhere or not hold nowhere, therefore this constant function is a realizer.
22.
Concerning the two reverts, I am mainly concerned with it being properly placed in the " metatheory " category with the rest, and I will be doing that presently.
23.
Like the object theory, the metatheory should be disciplined, perhaps even quasi-formal itself, but in general the interpretations of objects and rules are intuitive rather than formal.
24.
Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metatheory but not the object theory.
25.
Unlike theorems proved within a given formal system, a metatheorem is proved within a metatheory, and may reference concepts that are present in the metatheory but not the object theory.
26.
The hereditarily countable sets form a model of Kripke Platek set theory with the axiom of infinity ( KPI ), if the axiom of countable choice is assumed in the metatheory.
27.
Together with his late wife, Margret Baltes, he proposed a systemic metatheory of ontogeny which characterizes lifespan development as the orchestration of three processes : selection, optimization, and compensation.
28.
Such a metatheory is simply inadequate wrt the question you are discussing, it is meaningless to ask whether it proves categoricity of second-order arithmetic when it cannot even formulate it.
29.
:You didn't specify what axiom system for arithmetic modulo " n " you have in mind, and you didn't specify the power of your metatheory.
30.
I am fairly confident that categoricity of second-order arithmetic is provable in any reasonable metatheory where it is expressible . J . 17 : 11, 23 October 2009 ( UTC)
