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Definitionen: (∃x,y) φx ∙ φy
≝ (∃α,α)φα
(∃x,y,z) φx ∙ φyφz
≝
(∃α,α,α)φα
etc. ⌊.⌋
allgemein: [(∃x,y) φx ∙ φy,
= (∃α,α)φα,
(∃–) ∙ – =
(∃–)φα,
(∃–ξ) ∙ – ∙ φξ
=
= (∃–,α)φα]
Dann wäre die allgemeine Form von (∃α)φα,
(∃α,α)φα,
etc:
[(∃α)φα,
(∃–) ∙ φα,
(∃–,α) ∙ φα]
(∃α)φα
∙
~(∃α,α) ∙ φα
= (Nα)φα
(∃α,[)|α])φα
∙
~(∃ααα)φα =
(Nα,α)φα
[(∃α)φα
∙
~(∃α,α) ∙ φα
= (Nα)φα,
(∃–)φα ∙
~(∃–)φα =
(N–)φα,
(∃–,α)φα
∙
∙ ~(∃–,α)φα =
N(–,α)φα]
So wäre das Zeichen N(…)φα
einzuführen.
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