Embedding the diamond lattice in the recursively enumerable truthtable degrees
HTML articles powered by AMS MathViewer
 by Carl G. Jockusch and Jeanleah Mohrherr PDF
 Proc. Amer. Math. Soc. 94 (1985), 123128 Request permission
Abstract:
It is shown that the four element Boolean algebra can be embedded in the recursively enumerable truthtable degrees with least and greatest elements preserved. Corresponding results for other lattices and other reducibilites are also discussed.References

P. Fejer and R. Shore, Embedding recursively presented lattices into the r.e. ttdegrees (to appear).
 Carl G. Jockusch Jr., Semirecursive sets and positive reducibility, Trans. Amer. Math. Soc. 131 (1968), 420–436. MR 220595, DOI 10.1090/S00029947196802205957
 A. H. Lachlan, Some notions of reducibility and productiveness, Z. Math. Logik Grundlagen Math. 11 (1965), 17–44. MR 172795, DOI 10.1002/malq.19650110104
 A. H. Lachlan, A note on universal sets, J. Symbolic Logic 31 (1966), 573–574. MR 211857, DOI 10.2307/2269692
 A. H. Lachlan, Lower bounds for pairs of recursively enumerable degrees, Proc. London Math. Soc. (3) 16 (1966), 537–569. MR 204282, DOI 10.1112/plms/s316.1.537
 Piergiorgio Odifreddi, Strong reducibilities, Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 1, 37–86. MR 590818, DOI 10.1090/S027309791981148631
 David B. Posner, The upper semilattice of degrees $\leq {\bf 0}^{\prime }$ is complemented, J. Symbolic Logic 46 (1981), no. 4, 705–713. MR 641484, DOI 10.2307/2273220
 Hartley Rogers Jr., Theory of recursive functions and effective computability, McGrawHill Book Co., New YorkToronto, Ont.London, 1967. MR 0224462
 J. R. Shoenfield, Quasicreative sets, Proc. Amer. Math. Soc. 8 (1957), 964–967. MR 89808, DOI 10.1090/S00029939195700898087
 Robert I. Soare, Fundamental methods for constructing recursively enumerable degrees, Recursion theory: its generalisation and applications (Proc. Logic Colloq., Univ. Leeds, Leeds, 1979) London Math. Soc. Lecture Note Ser., vol. 45, Cambridge Univ. Press, CambridgeNew York, 1980, pp. 1–51. MR 598302
 Paul R. Young, On semicylinders, splinters, and boundedtruthtable reducibility, Trans. Amer. Math. Soc. 115 (1965), 329–339. MR 209151, DOI 10.1090/S00029947196502091511
Additional Information
 © Copyright 1985 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 94 (1985), 123128
 MSC: Primary 03D25
 DOI: https://doi.org/10.1090/S00029939198507810693
 MathSciNet review: 781069