Ψ₀(Ωω)

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

  • , 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
gollark: In any case, this may be irrelevant, because new CPUs will be out in 1-3 years.
gollark: Well, GPUs are meant to run on 16 PCIe lanes though apparently work on 8.
gollark: (Ryzen is better anyway)
gollark: So I think what it'd do is either not work or bring your GPU down to 8 lanes.
gollark: https://ark.intel.com/products/126687/Intel-Core-i5-8400-Processor-9M-Cache-up-to-4-00-GHz-

References

  • G. Takeuti, Proof theory, 2nd edition 1987 ISBN 0-444-10492-5
  • K. Schütte, Proof theory, Springer 1977 ISBN 0-387-07911-4
  • Simpson, Stephen G. (2009), Subsystems of second order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, ISBN 978-0-521-88439-6, MR 2517689


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