Lattice embeddings in the recursively enumerable truth table degrees
Christine Ann Haught · Transactions of the American Mathematical Society · 1987
It is shown that every finite lattice, and in fact every recursively presentable lattice, can be embedded in the r.e. tt \text {tt} -degrees by a map preserving least and greatest elements. The decidability of the 1 1 -quantifier theory of the r.e. tt \text {tt} -degrees in the language with ⩽ , ∨ , ∧ , 0 \leqslant ,\, \vee ,\, \wedge ,\,0 , and 1 is obtained as a corollary.