Logichard
0:00.0

In model theory, the spectrum of a first-order sentence ϕ\phi is the set of all positive integers nn such that ϕ\phi has a model of cardinality nn. Consider the sentence ϕ\phi in a signature containing a single unary function symbol ff: ϕ=x(f(f(f(x)))=xf(x)x)\phi = \forall x (f(f(f(x))) = x \land f(x) \neq x) Which of the following describes the spectrum of ϕ\phi?