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 J(ωω(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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