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Not to be confused with Joycian tetratri.

Joyce's tetratri is equal to \(\text g(2,1,1,4,3,3)\) in Joyce's More Generalized Exponential Notation.[1][2] The value was created by Andre Joyce as a failed attempt to define the Bowersism tetratri, which is much larger. In arrow notation, it is equal to 3^^^^(3^^^3-1 ^'s)^^^^^3. This number is closer to tritriplex.

Approximations

Notation Approximation
BEAF {3,3,{3,3,3}-1} (exact)
Hyper-E notation E3##3#2
X-Sequence Hyper-Exponential Notation 3{X}(3{X}3-1)
Fast-growing hierarchy \(f_{\omega}(f_4(3))\)
Hardy hierarchy \(H_{\omega^{\omega}+\omega^4}(3))\)
Slow-growing hierarchy \(g_{\varphi(\zeta_0,0)}(3)\)

Sources

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