Side nesting (横ネスト in Japanese) is a method to generate a googological system introduced by a Japanese googologist mrna. It admits a generalisation called shifting definition.
One of the most characteristic and confusing feature of side nesting is that even if a notation employs \(+\) as a \(2\)-ary function symbol, it does not necessarily work as the addition. Namely, even if a valid expression \(a\) corresponds to a countable ordinal \(\alpha\) and \(a + a\) is also a valid expression, \(a + a\) does not necessarily corresponds to \(\alpha + \alpha\). The characteristic feature of side nesting on \(+\) is inherited by its generalisation shifting definition. If a notation based on side nesting does not employ \(+\), then a separator plays the role analogous to \(+\) in a notation based on side nesting.
According to mrna, side nesting is a method which can be found in many notations, while there are few notations which intensionally focus on side nesting. The following three systems are intended to be based on side nesting:
Although none of them has been fully defined, many Japanese googologists get interested to their intended behaviour, because they are expected to be poweful. For the detail explanation of the strength, see the following subsections:
- Main article: SSAN
- Main article: S-σ
S-σ is a notation introduced by mrna as a system purely based on side nesting, while SSAN also employs another strategy than side nesting.
- Main article: Y function