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Realization of φ -types and Keisler’s order

M. E. Malliaris

Annals of Pure and Applied Logic 157 (2-3):220-224 (2009)

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On ◁∗-maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.details This paper investigates a connection between the semantic notion provided by the ordering * among theories in model theory and the syntactic SOPn hierarchy of Shelah. It introduces two properties which are natural extensions of this hierarchy, called SOP2 and SOP1. It is shown here that SOP3 implies SOP2 implies SOP1. In Shelah's article 229) it was shown that SOP3 implies -maximality and we prove here that -maximality in a model of GCH implies a property called SOP2″. It has been (...) Download Export citation Bookmark 31 citations
Saturation of ultrapowers and Keisler's order.Saharon Shelah - 1972 - Annals of Mathematical Logic 4 (1):75.details Download Export citation Bookmark 4 citations
Toward classifying unstable theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.details Download Export citation Bookmark 43 citations
Ultraproducts which are not saturated.H. Jerome Keisler - 1967 - Journal of Symbolic Logic 32 (1):23-46.details In this paper we continue our study, begun in [5], of the connection between ultraproducts and saturated structures. IfDis an ultrafilter over a setI, andis a structure, the ultrapower ofmoduloDis denoted byD-prod. The ultrapower is important because it is a method of constructing structures which are elementarily equivalent to a given structure. Our ultimate aim is to find out what kinds of structure are ultrapowers of. We made a beginning in [5] by proving that, assuming the generalized continuum hypothesis, for (...) Download Export citation Bookmark 24 citations

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