Peano arithmetic may not be interpretable in the monadic theory of linear orders
Journal of Symbolic Logic 62 (3):848-872 (1997)
Abstract
Gurevich and Shelah have shown that Peano Arithmetic cannot be interpreted in the monadic second-order theory of short chains (hence, in the monadic second-order theory of the real line). We will show here that it is consistent that the monadic second-order theory of no chain interprets Peano ArithmeticLinks
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References found in this work
Undecidable Theories.Alfred Tarski, Andrzej Mostowski & Raphael M. Robinson - 1953 - Philosophy 30 (114):278-279.
Second-order quantifiers and the complexity of theories.J. T. Baldwin & S. Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (3):229-303.
Monadic theory of order and topology in ZFC.Yuri Gurevich & Saharon Shelah - 1982 - Annals of Mathematical Logic 23 (2-3):179-198.
