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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...
We construct a recursive class of trees having decidable theories in Lo(Q1). Furthermore this class is a dense class of trees. The methods which we use are similar to those of H. Läuchli and J.Leonhard [4]. From our construction the decidability of TR(X 1), the theory of uncountable trees in Lo(Q1), follows as a corollary. This was first proved by H.Herre
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