META THEOREM from AXIOMATIC SYSTEM by TELEKINETT / MAURICIO REYES

A meta theorem is a statement about a formal system proven in a metalanguage. Unlike theorems proved within a given formal system, a meta theorem is proved within a metatheory and may reference concepts that are present in the metatheory but not the object theory.[citation needed]

A formal system is determined by a formal language and a deductive system (axioms and rules of inference). The formal system can be used to prove particular sentences of the formal language with that system. Metatheorems, however, is proved externally to the system in question, in its metatheory. Common metatheories used in logic are set theory (especially in model theory) and primitive recursive arithmetic (especially in proof theory). Rather than demonstrating particular sentences to be provable, meta theorems may show that each of a broad class of sentences can be proved, or show that certain sentences cannot be proved.[citation needed]

Mauricio Reyes is a futurist, composer and audio researcher focused on experimental, electronic, and electroacoustic practices.

Founder of Telekinett Records (2004–2008), a label dedicated to atonal and exploratory sound, he investigates signal behavior, noise systems, and spatial perception through granular synthesis, tape manipulation, spectral analysis, and circuit experimentation.