Three red herrings around Vaught’s conjecture
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- by John T. Baldwin, Sy D. Friedman, Martin Koerwien and Michael C. Laskowski PDF
- Trans. Amer. Math. Soc. 368 (2016), 3673-3694 Request permission
Abstract:
We give a model theoretic proof that if there is a counterexample to Vaught’s conjecture there is a counterexample such that every model of cardinality $\aleph _1$ is maximal (strengthening a result of Hjorth’s). In the process we analyze three examples of a sentence characterizing $\aleph _1$. We also give a new proof of Harrington’s theorem that any counterexample to Vaught’s conjecture has models in $\aleph _1$ of arbitrarily high Scott rank below $\aleph _2$.References
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Additional Information
- John T. Baldwin
- Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan St. (M/C 249), Chicago, Illinois 60607-7045
- Sy D. Friedman
- Affiliation: Kurt Gödel Research Center for Mathematical Logic, Universität Wien, Währinger Strasse 25, 1090 Wien, Austria
- MR Author ID: 191285
- Martin Koerwien
- Affiliation: Kurt Gödel Research Center for Mathematical Logic, Universität Wien, Währinger Strasse 25, 1090 Wien, Austria
- Michael C. Laskowski
- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-4015
- Received by editor(s): November 21, 2013
- Received by editor(s) in revised form: September 17, 2014
- Published electronically: November 6, 2015
- Additional Notes: The research of the first author was partially supported by Simons travel grant G5402 and the Austrian Science Fund (FWF)
The research of the second author was supported by FWF (Austrian Science Fund) Grant P24654-N25.
The research of the third author was supported by the Austrian Science Fund (FWF) Lise Meitner Grant M1410-N25
The fourth author was partially supported by NSF grant DMS-1308546 - © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 3673-3694
- MSC (2010): Primary 03C15, 03C55, 03C75, 03E40
- DOI: https://doi.org/10.1090/tran/6572
- MathSciNet review: 3451890