Sasquatch is a googologism based on an extension of the language of set theory. It was defined on 27th March 2017 by wikia user Emlightened.[1] It is also called Big Bigeddon. It would have been the largest valid googolism, but the community could not understand it. Thus, that honor was given to Little Bigeddon. However, it turned out that their definitions include serious ambiguity and many errors.

Definition of Sasquatch

We work in the language \((\in, \bar\in, <)\), where equality is a defined symbol. \(\in\), \(\bar\in\) and \(<\) are binary predicates, we also define the unary functions \(F\) and \(R\) from these.

We then define the Sasquatch as the largest number \(k\) such that there is some unary formula \(\phi\) in the language \(\{\bar\in,Q\}\) (where \(Q(a,b) \leftrightarrow R(a)=b\)) of quantifier rank \(\leq 12\uparrow\uparrow 12\) such that \(\exists ! a (\phi(a)) \wedge \phi(k)\).

Issues

The definition contains many errors pointed by Japanese Googology Wiki user p進大好きbot. For example, \(R\) is defined after setting the condition "\((\bar\in,R,F)\vDash t\text{ is an ordinal}\)", and this causes circular logic. Also, \(F\) is defined in a similar way. Maybe they are just abuses of notation for the author, but the precise meanings are quite ambiguous. For example, \(R(t)\) should be denoted as \(f(\bar\in,R,F,t)\) for a new function symbol \(f\) because its definition depends on \((\bar\in,R,F)\).

Moreover, formulae in the language \(\{\bar\in,Q\}\) does not admit an interpretation in \((V,\in)\). Therefore the truth of such formulae, which are used in the definition of Sasquatch, does not make sense. As a conclusion, Sasquatch is ill-defined.

Sources

  1. Emlightened. Sasquatch

See also

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