"The ω-inconsistency and overspill in Cantor-Łukasiewicz set theory"

logic 拙論

13:30-15:00、科学アカデミーのボルツァーノ・ホールにて(下画像は会場の風景)。

L∀上の包括原理を持つ集合論で展開される算術について、既存の結果のサーベイ、聴衆は7人。要旨は以下の通り。

  • Set theory:
    • Cantor-Łukasiewicz set theory CŁ0 with the comprehension principle within Łukasiewicz predicate logic Ł∀.
    • H with the comprehension principle within　Łukasiewicz infinite-valued predicate logic ∀Ł
  • Known:
    • Mathematical induction on ω implies a contradiction in CŁ0 by a very long proof [H04].
    • Mathematical induction on ω implies a contradiction in H by a simple proof [Y05].
  • We will show
    • mathematical induction on ω implies a contradiction in CŁ0 by a simple proof,
    • the arithmetic developed in CŁ0 is somehow similar to the one developed in the non-standard model of PA.

ベヘロフカを直前に飲まされた割には好評でした。