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The Lindenbaum-algebra of the theory of well-orders and Abelian groups with the quantifier Qα

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Part of the Lecture Notes in Mathematics book series (LNM,volume 619)

Abstract

If τ is any linear order type, let J(τ) be the Boolean algebra generated by the left-closed right-open (including [x, ∞)) intervals of τ.

It will be shown that the Lindenbaum-algebra of the theory of well-orders with the quantifier "there exists X α many" (Qα) is isomorphic to Jω(1+η)) and of the theory of Abelian groups is isomorphic to J((1+η+ωω(1+η))(1+η)) for α=0 and isomorphic to J((1+η+ωω)(1+η)) for α>0.

Keywords

  • Abelian Group
  • Boolean Algebra
  • Order Type
  • Structure Diagram
  • Boolean Combination

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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© 1977 Springer-Verlag

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Baudisch, A., Weese, M. (1977). The Lindenbaum-algebra of the theory of well-orders and Abelian groups with the quantifier Qα . In: Lachlan, A., Srebrny, M., Zarach, A. (eds) Set Theory and Hierarchy Theory V. Lecture Notes in Mathematics, vol 619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067642

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  • DOI: https://doi.org/10.1007/BFb0067642

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08521-8

  • Online ISBN: 978-3-540-37032-1

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