Independence, order, and the interaction of ultrafilters and theories

Annals of Pure and Applied Logic 163 (11):1580-1595 (2012)

Abstract
We consider the question, of longstanding interest, of realizing types in regular ultrapowers. In particular, this is a question about the interaction of ultrafilters and theories, which is both coarse and subtle. By our prior work it suffices to consider types given by instances of a single formula. In this article, we analyze a class of formulas φ whose associated characteristic sequence of hypergraphs can be seen as describing realization of first- and second-order types in ultrapowers on one hand, and properties of the corresponding ultrafilters on the other. These formulas act, via the characteristic sequence, as points of contact with the ultrafilter D, in the sense that they translate structural properties of ultrafilters into model-theoretically meaningful properties and vice versa. Such formulas characterize saturation for various key theories , yet their scope in Keisler’s order does not extend beyond Tfeq. The proof applies Shelah’s classification of second-order quantifiers
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2011.12.010
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 40,625
Through your library

References found in this work BETA

Toward Classifying Unstable Theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.
Simple Unstable Theories.Saharon Shelah - 1980 - Annals of Pure and Applied Logic 19 (3):177.
On ◁∗-Maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.
Realization of Φ -Types and Keisler’s Order.M. E. Malliaris - 2009 - Annals of Pure and Applied Logic 157 (2-3):220-224.
More on SOP 1 and SOP 2.Saharon Shelah & Alexander Usvyatsov - 2008 - Annals of Pure and Applied Logic 155 (1):16-31.

View all 13 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Ultrafilters on Ω.James E. Baumgartner - 1995 - Journal of Symbolic Logic 60 (2):624-639.
Hypergraph Sequences as a Tool for Saturation of Ultrapowers.M. E. Malliaris - 2012 - Journal of Symbolic Logic 77 (1):195-223.
Ultrafilters Which Extend Measures.Michael Benedikt - 1998 - Journal of Symbolic Logic 63 (2):638-662.
A Characterization of 2-Square Ultrafilters.Ned I. Rosen - 1983 - Journal of Symbolic Logic 48 (2):409-414.
Properties and Consequences of Thorn-Independence.Alf Onshuus - 2006 - Journal of Symbolic Logic 71 (1):1 - 21.
On Milliken-Taylor Ultrafilters.Heike Mildenberger - 2011 - Notre Dame Journal of Formal Logic 52 (4):381-394.
Reasonable Ultrafilters, Again.Andrzej Rosłanowski & Saharon Shelah - 2011 - Notre Dame Journal of Formal Logic 52 (2):113-147.
What Is True and False About So-Called Theories of Truth?Jaakko Hintikka - 2000 - The Proceedings of the Twentieth World Congress of Philosophy 2000:155-160.
Independence Accounts of Substance and Substantial Parts.Patrick Toner - 2011 - Philosophical Studies 155 (1):37 - 43.
Saturating Ultrafilters on N.D. H. Fremlin & P. J. Nyikos - 1989 - Journal of Symbolic Logic 54 (3):708-718.

Analytics

Added to PP index
2013-10-27

Total views
21 ( #390,538 of 2,242,336 )

Recent downloads (6 months)
7 ( #255,374 of 2,242,336 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature