Theoremet

Theoremet is a fictional or hypothetical concept used as a thought experiment in mathematical logic. It is not a standard term in formal mathematics, but is sometimes employed to discuss meta-level properties of theorems themselves. In this sense, theoremet refers to a statement about theorems rather than a statement about objects within a particular theory.

Definition and scope: A theoremet is any proposition that concerns attributes of theorems in a fixed formal system S. Such a statement may describe derivational features, proof lengths, dependencies on axioms, or relationships among theorems. A theoremet can be formulated as a property P(T) that a theorem T satisfies, or as a universal claim about all theorems derivable in S, for example “every theorem of S has a finite proof in a given encoding.”

Purpose and use: The concept is intended to explore questions about meta-theoretic structure without tying them to established results. Theoremet can be used to illustrate how one might reason about the set of theorems, the nature of provability, or the limits of derivations within a formal system. Because it is not part of standard theory, the truth of a theoremet depends on its precise formulation and the underlying system S.

Examples: In a toy formalism, a theoremet might state that every theorem has a bounded proof length. Another fictional theoremet could claim that theorems of S are closed under a specified transformation, or that theorems constitute a decidable set under a particular decision procedure. These examples are illustrative rather than canonical results.

Relation to established notions: The name resembles metatheorems or meta-theory, but theoremet is not an established, formal notion in standard logic. It serves to prompt discussion about how theorems themselves might be characterized at a higher level.

See also: Theorem, Metatheory, Meta-theorem, Gödel’s incompleteness theorem.