The P-T-degrees of the recursive sets: lattice embeddings, extensions of embeddings and the two quantifier theory

It has been shown in the literature that the two basic nondistributive lattices can be embedded in R/sub pt/, the polynomial-time turing degrees of the recursive sets. The authors introduce more general techniques to extend these results to show that every recursive lattice can be embedded in R/sub pt/. In addition to lattice theoretic representation theorems, they use the scheme of priority style arguments coupled with looking back techniques. They also generalize the density-type results to settle the full extension of the embeddings problem for R/sub pt/. Combined with the logical analysis of sentences with one alternation of quantifiers, these results suffice to decide the full For all There exists -theory of R/sub pt/. They also give a strong nonhomogeneity result.<
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