goo

「収穫と蒔いた種と」について。2

2021-01-25 06:59:50 | Mathematics
Put X"=X∪{(1∈N")∧∀x∀y(((x∈N")→(x+1∈N"))∧((x∈N")∧(y∈N")→(x≥y)∨(y≥x))∧
((x≥y)↔((x=y)∨∃z((z∈N")∧(x=y+z))))∧(ax∈A-{0}))} and Y=X"∪{d∈A-{0},T(A,A(d/an) |M |= n∈N"}.
If Y isn't consistent ∃n1…∃nm(X"∪{d∈A-{0},T(A,A(d/an1),…,T(A,A(d/anm} |- 1≠1).
But this axiom system has a model in which d=amax{n1,…,nm}+1 and is consistent. So Y is consistent and has a model
M" if X" is consistent. Let S" be the object domain of M" {A(d/an) | n∈N"}∈S.
M" |= ∃n((n∈N")∧(A(d/an)=A(d/an+1))) M" |= ∃a"((a"∈A)∧(a"a=1). This is contradiction. X" isn't consistent.
The standard mathematics treating Noetherian domain (A) and the natural numbers (N") isn't consistent.

The theorems which are the type of "If F is a field, F[x1,…xm] is …." are false
for k is a field and C=k[x1,…,xm] doesn't exists if X is consistent.
Put C"=k[[x1,…,xm]]. If C" exists, P"={f |(f∈C")∧(∃n(f=x1n))} and N={n |x1n∈P} exists.
C"doesn't exists like C .
ch(A")=ch(k)=0.You may think that c∈Z⇒c∈A" and c∈Q ⇒ c∈k.

'70's にはフランスでは知られた事だったら
しいです。
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