Ordinal de Takeuti-Feferman-Buchholz

En utilisant la notation psi de Buchholz, l'ordinal $\psi_0(\varepsilon_{\Omega_\omega+1})$, généralement appelé l'ordinal de Takeuti-Feferman-Buchholz, est un grand ordinal dénombrable qui est l'ordinal de la théorie de la preuve de $\Pi^1_1$-CA+BI, a subsystem of second-order arithmetic. C'est aussi l'ordinal de la théorie de la preuve de $\Pi^1_1$-comprehension+transfinite induction In googology, the ordinal is abbreviated to TFBO. Il est différent de en:Buchholz's ordinal, qui est abrégé en BO.

Propriété

It is the limit of en:Feferman's theta function, as well as the limit of the fonction de Buchholz. It is the order type of D₁0 in en:Buchholz's ordinal notation (OT,<).

It is also the ordinal measuring the strength of l'hydre de Buchholzs with ω labels, as well as the upper bound of the SCG function.

It was named by David Madore under the nickname "Gro-Tsen" on wikipedia.