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Quasimaximality and principal filters isomorphism between

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Abstract.

Let I be a quasimaximal subset of a computable basis of the fully efective vector space V ∞ . We give a necessary and sufficient condition for the existence of an isomorphism between the principal filter respectivelly. We construct both quasimaximal sets that satisfy and quasimaximal sets that do not satisfy this condition. With the latter we obtain a negative answer to Question 5.4 posed by Downey and Remmel in [3].

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References

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  2. Downey, R.G.: Undecidability of ℒ(F ∞ ) and other lattices of r.e. substructures. Ann. Pure Appl. Logic 32~(1), 17–26 (1986); corr. ibid. 48, 299–301 (1990)

  3. Downey, R.G., Remmel, J.B.: Computable Algebras and Closure Systems: Coding Properties. Handbook of recursive mathematics, Vol. 2, Stud. Logic Found. Math., 139, North-Holland, Amsterdam, 1998, pp. 977–1039

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Authors and Affiliations

  1. Department of Mathematics, Western Illinois University, Macomb, IL 61455, USA

    Rumen Dimitrov

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  1. Rumen Dimitrov
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Correspondence to Rumen Dimitrov.

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Based on the author’s Ph.D. dissertation.

Mathematics Subject Classification (2000): 03D25, 03C57

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Dimitrov, R. Quasimaximality and principal filters isomorphism between . Arch. Math. Logic 43, 415–424 (2004). https://doi.org/10.1007/s00153-003-0196-9

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  • DOI: https://doi.org/10.1007/s00153-003-0196-9

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