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Interpreting second-order logic in the monadic theory of order. (English) Zbl 0559.03008
Assuming that for every cardinal $$\lambda$$ there is a regular cardinal $$\kappa >\lambda$$ such that $$\Sigma \{2^{\mu}|$$ $$\mu <\kappa \}$$ is equal to $$\kappa$$, one assigns effectively a sentence $$\phi$$ ’, in the monadic language of order to an arbitrary second-order sentence $$\phi$$ in such a way that every nonempty set satisfies $$\phi$$ iff every chain satisfies $$\phi$$ ’. As a consequence, it follows that the second-order logic is interpretable in the monadic theory of order.
Reviewer: D.Lucanu

##### MSC:
 03B15 Higher-order logic; type theory (MSC2010) 06A05 Total orders 03B25 Decidability of theories and sets of sentences
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##### References:
 [1] DOI: 10.2307/1971037 · Zbl 0345.02034 [2] Transactions of the American Mathematical Society 141 pp 1– (1969) [3] DOI: 10.1007/BF02761824 · Zbl 0428.03034 [4] Annals of Mathematical Logic [5] Abstract model theory and stronger logics [6] Set theory (1978)
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