Open Access
2015 Vaught’s Conjecture Without Equality
Nathanael Leedom Ackerman
Notre Dame J. Formal Logic 56(4): 573-582 (2015). DOI: 10.1215/00294527-3153588


Suppose that σLω1,ω(L) is such that all equations occurring in σ are positive, have the same set of variables on each side of the equality symbol, and have at least one function symbol on each side of the equality symbol. We show that σ satisfies Vaught’s conjecture. In particular, this proves Vaught’s conjecture for sentences of Lω1,ω(L) without equality.


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Nathanael Leedom Ackerman. "Vaught’s Conjecture Without Equality." Notre Dame J. Formal Logic 56 (4) 573 - 582, 2015.


Received: 18 October 2012; Accepted: 26 September 2013; Published: 2015
First available in Project Euclid: 30 September 2015

zbMATH: 1372.03057
MathSciNet: MR3403092
Digital Object Identifier: 10.1215/00294527-3153588

Primary: 03C15 , 03C75
Secondary: 03C30

Keywords: equality , Infinitary logic , Martin’s conjecture , Vaught’s conjecture

Rights: Copyright © 2015 University of Notre Dame

Vol.56 • No. 4 • 2015
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