Journal of Mathematical Logic 12 (1):1250001- (2012)
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We prove two results on the stability spectrum for Lω1,ω. Here [Formula: see text] denotes an appropriate notion of Stone space of m-types over M. Theorem for unstable case: Suppose that for some positive integer m and for every α μ, K is not i-stable in μ. These results provide a new kind of sufficient condition for the unstable case and shed some light on the spectrum of strictly stable theories in this context. The methods avoid the use of compactness in the theory under study. In this paper, we expound the construction of tree indiscernibles for sentences of Lω1,ω. Further we provide some context for a number of variants on the Ehrenfeucht–Mostowski construction.
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DOI | 10.1142/S0219061312500018 |
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References found in this work BETA
Model Theory for Infinitary Logic: Logic with Countable Conjunctions and Finite Quantifiers.H. Jerome Keisler - 1971 - Amsterdam: North-Holland Pub. Co..
On ◁∗-Maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.
Shelah's Stability Spectrum and Homogeneity Spectrum in Finite Diagrams.Rami Grossberg & Olivier Lessmann - 2002 - Archive for Mathematical Logic 41 (1):1-31.
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Citations of this work BETA
Tree Indiscernibilities, Revisited.Byunghan Kim, Hyeung-Joon Kim & Lynn Scow - 2014 - Archive for Mathematical Logic 53 (1-2):211-232.
Axiomatizing Changing Conceptions of the Geometric Continuum II: Archimedes-Descartes-Hilbert-Tarski†.John T. Baldwin - 2019 - Philosophia Mathematica 27 (1):33-60.
Characterization of NIP Theories by Ordered Graph-Indiscernibles.Lynn Scow - 2012 - Annals of Pure and Applied Logic 163 (11):1624-1641.
Indiscernibles, EM-Types, and Ramsey Classes of Trees.Lynn Scow - 2015 - Notre Dame Journal of Formal Logic 56 (3):429-447.
Completeness and Categoricity (in Power): Formalization Without Foundationalism.John T. Baldwin - 2014 - Bulletin of Symbolic Logic 20 (1):39-79.
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