In any system many axiomatic true(s) are found just by finding the nature of any particular thing. So in determining the nature of any particular thing many axiomatic true(s) are invariably found. An axiomatic true for any human is: ‘every human is alive’. Other axiomatic true(s) may be implied, for example, for a human, all these are implied axiomatic true(s): ‘humans have a mind’ or ‘humans have a body’ or ‘humans have a face’. And many more. Other axiomatic true(s) may be undeterminable or impossible to know with available knowledge (such as possibilities when more than one possible outcome)– but, for an inanimate object or something inherently dead – say, a rock, if we know inherently that all rocks are hard and that all rocks are not alive – then the axiomatic true(s) are ‘all rocks are hard’ and ‘all rocks are NOT alive’ – just because that’s inherently what a rock is. Inherent things are always axiomatic trues…– the other true(s) may or may not be determinable with our given knowledge… However, all axiomatic knowledge is not determinable by Just knowing the nature of a particular thing – there are still undeterminable axiomatic true(s) that take more knowledge than Just the nature. For example, I cannot determine axiomatic true(s) when there is more than one possibility that can happen – it would be non-predictable.
How much would axiomatically exist in infinity? And is resurrection an axiomatic function or consequence of all states ALREADY existing in nature …. Is it in the nature of infinity to axiomatically have A perfect copy of you (down to consciousness and memories) - and all your POSSIBLE states–? Because it would be easier for infinity to make all POSSIBLE states (because infinity is infinitely axiomatic) than to make just your current version? In fact, the later would be impossible - it is in the nature of infinity to be infinitely axiomatic - ALL states NOT specific ones.
First of all you need to do research into logic, your language shows you need to go study logic and play around with it first.
Axioms are merely shapes, data shapes in fact, they are informational geometry shapes, in ‘dataspace’.
Think of a cookie cutter: that the boundary-shape defines the axiom, and defines what can be ‘derived’ from the cookie cutter.
There are infinitely many axioms, and infinitely many independent, and dependent sets.
Are there ALWAYS axioms, or do they cease when you die? You said, basically, they are by-products of natures. So are there axioms to the nature of death?
Axioms are simply the result of distinct objects. So yeah there are always axioms. If anything exists, it must belong to the exist axiomatic set 
Imagine an ALL white piece of paper, now put a dot on it, the axiom is created the moment a geometric distinction was created.