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Hierarchies of Boolean algebras

  • Lawrence Feiner (a1)

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A denumerable structure is said to be recursive iff its universe is a recursive subset of the natural numbers and its relations and operations are recursive. For example, the standard model of number theory is recursive. A structure is said to be recursively presentable iff it is isomorphic to a recursive structure. For example, a Boolean algebra generated by ℵ0 free generators is easily seen to be recursively presentable. (For basic facts concerning Boolean algebras, the reader is referred to R. Sikorski [9] and A. Tarski and A. Mostowski [10].)

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[1]Davis, M., Computability and unsolvability, McGraw-Hill, New York, 1958.
[2]Feiner, L., Orderings and Boolean algebras not isomorphic to recursive ones, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1967.
[3]Hanf, W., Isomorphism in elementary logic, Notices of the American Mathematical Society, vol. 9 (1962), pp. 127128.
[4]Hanf, W., Model theoretic methods in the study of elementary logic, The theory of models, North-Holland, Amsterdam, 1965, pp. 133146.
[5]Hanf, W., On some fundamental problems concerning isomorphism of Boolean algebras, Mathematicae scandinavica, vol. 5 (1957), pp. 205217.
[6]Lachlan, A., On the lattice of recursively enumerable sets, Transactions of the American Mathematical Society, vol. 130 (1968), pp. 137.
[7]Rabin, M., On recursively enumerable and arithmetic models of set theory, this Journal, vol. 23 (1958), pp. 408416.
[8]Rogers, H., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.
[9]Sikorski, R., Boolean algebra, Springer-Verlag, Berlin, 1964.
[10]Tarski, A. and Mostowski, C., Boolesche Ringe mit geordneter Basis, Fundamenta mathematicae, vol. 32 (1939).
[11]Tennenbaum, S., Non-Archimedean models for arithmetic, Notices of the American Mathematical Society, vol. 6 (1959), p. 207.

Hierarchies of Boolean algebras

  • Lawrence Feiner (a1)

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