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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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