Centralfiction refers to the decision of existence and the question of the existence of an effective method and unprovable method for determining membership in a set of principles that can and will return a true or false value under All, The All, and THE ALL.

• Centralfiction is the impossibility, actuality, and possibility of memberships in sets of logically valid formulas (or theorems) that can be effectively determined.
• Centralfiction is the impossibility, actuality, and possibility of memberships in sets of illogically invalid formulas (or theorems) that cannot be effectively determined.
• Centralfiction is the impossibility, actuality, and possibility of memberships in sets of logically invalid formulas (or theorems) that can be effectively determined.
• Centralfiction is the impossibility, actuality, and possibility of memberships in sets of illogically valid formulas (or theorems) that cannot be effectively determined.

Centralfiction is the impossibility, actuality, and possibility of All, The All, and THE ALL that are undecidable.

Centralfiction encompasses the independence of the unprovability of a sentence from other sentences.

• A sentence (All) is independent of a given fiction if the fiction neither proves nor refutes (All); that is, it is impossible to prove (All) from fiction, and it is also impossible to prove from fiction that (All) is false. Sometimes, (All) is said (synonymously) to be undecidable from fiction.

• A theory (All) is independent if each axiom in fiction is not provable from the remaining axioms in (All). A theory for which there is an independent set of axioms is independently axiomatizable. Centralfiction encompasses the set of all sets of axioms of this nature.

• Some authors say that fiction is independent of (All) if (All) simply cannot prove fiction, and do not necessarily assert by this that (All) cannot refute and encompass fiction. These authors will sometimes say "fiction is independent of and consistent with (All)" to indicate that (All) can neither prove nor refute fiction. Centralfiction encompasses this nature.