Veblen function: Difference between revisions

Revision as of 09:14, 8 May 2023

Revision as of 01:17, 14 September 2023

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==Values==

The function takes on several prominent values:

* <math>\varphi(\omega,0)</math>, a bound on the order types of the [[Path ordering (term rewriting)|recursive path orderings]] with finitely many function symbols. <ref>MN. Dershowitz, NM. Okada, [https://www.cs.tau.ac.il/~nachumd/papers/ProofTheoretic.pdf Proof Theoretic Techniques for Term Rewriting Theory] (1988). p.105</ref>

* The [[Feferman-Schutte ordinal]] <math>\Gamma_0</math> is equal to <math>\varphi(1,0,0)</math>.<ref>D. Madore, "[http://www.madore.org/~david/math/ordinal-zoo.pdf A Zoo of Ordinals]" (2017). Accessed 02 November 2022.</ref>

* The [[small Veblen ordinal]] is equal to <math>\varphi\begin{pmatrix}1 \\ \omega\end{pmatrix}</math>. <ref>{{cite journal | url=https://link.springer.com/content/pdf/10.1007/s00153-019-00658-x.pdf | doi=10.1007/s00153-019-00658-x | title=A flexible type system for the small Veblen ordinal | year=2019 | last1=Ranzi | first1=Florian | last2=Strahm | first2=Thomas | journal=Archive for Mathematical Logic | volume=58 | issue=5–6 | pages=711–751 | s2cid=253675808 }}</ref>