The reduction presupposes that θ faithfully captures full second-order semantics, but Henkin models satisfying θ need not validate full comprehension, undermining the biconditional in P3.
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Second-order semantics(in logic and philosophy of language)
A way of talking about language where you can make statements not just about things in the world, but about the statements themselves—like commenting on the rules of the language rather than just using it.
reduction(Lambda calculus or term-rewriting systems)
A computational process analogous to computing the value of a function, proceeding through a series of discrete calculation steps applied to a term
θ (theta)(in formal logic notation)
A variable (placeholder) used to represent any logical statement or formula, like how 'x' represents an unknown number in algebra.