Notes on monadic logic. A: Monadic theory of the real line
type: Item
instance of: scholarly article
title: Notes on monadic logic. A: Monadic theory of the real line
zbMATH Open document ID: 0664.03034
DOI: 10.1007/BF02778038
author: S. Shelah
published in: Israel Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: In an earlier paper with \textit{Yu. Gurevich} [ibid. 49, 55-68 (1984; Zbl 0575.03028)] the author showed that (assuming CH) the second-order theory of the continuum in the Cohen extension of the universe has an interpretation in the monadic theory of the real line as well as in the monadic theory of any non-modest short chain. In this paper the author shows how this result can be obtained without CH.
Mathematics Subject Classification ID: 03E70
Mathematics Subject Classification ID: 03B25
Mathematics Subject Classification ID: 03C62
zbMATH DE Number: 4085636
zbMATH Keywords: monadic theory of non-modest short chain
zbMATH Keywords: second-order theory of the continuum
zbMATH Keywords: Cohen extension of the universe
zbMATH Keywords: monadic theory of the real line
reviewed by: J. M. Plotkin
MaRDI profile type: Publication
cites work: Second-order quantifiers and the complexity of theories
cites work: There may be simple \(P_{\aleph _ 1}\)- and \(P_{\aleph _ 2}\)-points and the Rudin-Keisler ordering may be downward directed
cites work: The monadic theory of ω2
cites work: Monadic theory of order and topology. II
cites work: Modest theory of short chains. II
cites work: Monadic theory of order and topology in ZFC
cites work: The monadic theory and the ''next world''
cites work: Interpreting second-order logic in the monadic theory of order
cites work: Q3757893
cites work: On the strength of the interpretation method
cites work: The decision problem for branching time logic
cites work: The monadic theory of order
cites work: Monadic logic and Löwenheim numbers
cites work: Around classification theory of models
description: scientific article; zbMATH DE number 4085636