Ψ₀(Ωω)

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The correct title of this article is Ψ0ω). It appears incorrectly here because of technical restrictions.

In mathematics, Ψ0ω) is a large countable ordinal that is used to measure the proof-theoretic strength of some mathematical systems. In particular, it is the proof theoretic ordinal of the subsystem -CA0 of second-order arithmetic; this is one of the "big five" subsystems studied in reverse mathematics (Simpson 1999).

Definition[edit]

  • , and for n > 0.
  • is the smallest set of ordinals that contains for n finite, and contains all ordinals less than , and is closed under ordinal addition and exponentiation, and contains if ji and and .
  • is the smallest ordinal not in

References[edit]