More on monadic logic. C: Monadically interpreting in stable unsuperstable \(\mathcal T\) and the monadic theory of \(^{\omega}\lambda\)
type: Item
instance of: scholarly article
title: More on monadic logic. C: Monadically interpreting in stable unsuperstable \(\mathcal T\) and the monadic theory of \(^{\omega}\lambda\)
zbMATH Open document ID: 0704.03016
DOI: 10.1007/BF02801469
author: S. Shelah
published in: Israel Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: [For Parts A and B see ibid. 63, No. 3, 335--352 (1988; Zbl 0664.03034) and ibid. 69, No. 1, 94--116 (1990; Zbl 0698.03034), respectively.] This paper contributes to the classification of pairs (\(\mathcal T,Q)\) where \(\mathcal T\) is a first order theory and \(Q\) is a quantifier. The main result concerns \(\mathcal T\) in a finite language which are stable but not superstable. For such \(\mathcal T\) ``one can, in monadic logic, interpret in it essentially trees \((^{\omega \geq}\lambda,<)\) with quantification \((Q^{pd}f)\) (on pressing down functions)''. Knowledge of earlier papers is required of the reader.
reviewed by: J. M. Plotkin
Mathematics Subject Classification ID: 03C45
zbMATH DE Number: 4154418
zbMATH Keywords: first order theory
zbMATH Keywords: quantifier
zbMATH Keywords: monadic logic
zbMATH Keywords: trees
zbMATH Keywords: pressing down functions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02801469
OpenAlex ID: W2086841212
description: scientific article; zbMATH DE number 4154418