Васил Пенчев
ТЕОРЕМАТА НА ГЕНЦЕН ЗА ТРАСФИНИТНО
ОБОСНОВАВАНЕ НА ПЕАНОВАТА АРИТМЕТИКА
Abstract: Gentzen’s completeness theorem of arithmetic by transfinite induction until ���� is
very important to us.
His argumentation was constructivist or even...
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Васил Пенчев
ТЕОРЕМАТА НА ГЕНЦЕН ЗА ТРАСФИНИТНО
ОБОСНОВАВАНЕ НА ПЕАНОВАТА АРИТМЕТИКА
Abstract: Gentzen’s completeness theorem of arithmetic by transfinite induction until ���� is
very important to us.
His argumentation was constructivist or even finitist’s one.
He claimed
that transfinite induction (contrary to its name) is a finitary method.
According to us, it is
mere the sequential undecidable statement.
We would prefer an «actualist» reinterpretation of
it: both finiteness and infinity until ���� together are dual and complementary.
Peano
arithmetic (including the principle of complete induction) can found infinity until ���� being the
metatheory or metalanguage of Gentzen arithmetic comprising both of the finite numbers
and infinite ordinals (less than ����).
In its turn, Gentzen arithmetic (i.
e.
Peano axiomatics,
in which complete induction is generalized to transfinite induction until ����) can found Peano
arithmetic being the metatheory or metalangug
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