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<div style="top: 600px; left: 800px; position: fixed; float: left;">
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<div style="top: 900px; left: 800px; position: fixed; float: left;">
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<div style="top: 600px; left: 1200px; position: fixed; float: left;">
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<div style="top: 900px; left: 1200px; position: fixed; float: left;">
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An ordinal \(\gamma\) is called an additive principal or additively principal if, for all \(\alpha, \beta < \gamma\), we have \(\alpha+\beta < \gamma\). The least additive principal ordinal is 1 since \(0 + 0 < 1\), and all additive principal ordinals other than 1 are limit ordinals. In particular, as can be seen from the Cantor normal form theorem (every ordinal has a [[Cantor normal form|CNF]] representation), additive principal ordinals are precisely the ordinals of the form \(\omega^\gamma\) for some ordinal \(\gamma\). As such, the second infinite additive principal ordinal is [[Omega^2|\(\omega^2\)]], the first limit of additive principal ordinals is [[Omega^omega|\(\omega^\omega\)]], and the first limit of the limits of additive principal ordinals is \(\omega^{\omega^2}\).
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