  It will be useful to identify the T-free fragment of a truth language L: the first-order language L− that has the same names, function symbols and relation symbols as L, except the unary predicate T. Since L− has the same names as L, including the same quote names, L− will have a quote name ‘A’ for every sentence A of L. Thus ∀xTx is not a sentence of L−, but ‘∀xTx’ is a name of L− and ∀x(x = ‘∀xTx’) is a sentence of L−. 