Special Session
Ackermann Function and Reverse Mathematics
Online
In 1928, Ackermann [1] defined one of the first examples of recursive but not primitive recursive functions. Later in 1935, Rózsa Péter [5] provided a simplification, which is now known as Ackermann or Ackermann-Péter function. The totality of Ackermann-Péter function is an interesting subject in the study of fragments of first order arithmetic. Kreuzer and Yokoyama [4] prove that the totality of Ackermann-Péter function is equivalent to a Σ3-proposition called PΣ1. And PΣ1 has played important roles in reverse mathematics in recent years. We will see some examples in this talk, including some joint works [2, 3] of the speaker and logicians in Singapore.
References
- [1]
- Ackermann, Wilhelm, Zum Hilbertschen Aufbau der reellen Zahlen, Mathematische Annalen, 99(1):118–133, 1928.
- [2]
- Chong, Chitat and Li, Wei and Wang, Wei and Yang, Yue, On the strength of Ramsey’s theorem for trees, Advances in Mathematics, 369:107180, 39 pp, 2020.
- [3]
- Chong, Chitat and Wang, Wei and Yang, Yue, Conservation Strength of The Infinite Pigeonhole Principle for Trees, Israel Journal of Mathematics, to appear, https://arxiv.org/abs/2110.06026.
- [4]
- Kreuzer, Alexander P. and Yokoyama, Keita, On principles between Σ1- and Σ2-induction, and monotone enumerations, Journal of Mathematical Logic, 16(1):1650004, 21 pp, 2016.
- [5]
- Péter, Rózsa, Konstruktion nichtrekursiver Funktionen, Mathematische Annalen, 111(1):42–60, 1935.
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