PP-2006-31: Sevenster, Merlijn and Tulenheimo, Tero (2006) Partially ordered connectives and Sigma-1-1 on finite models. [Report]
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Abstract
In this paper we take up the study of Henkin quantifiers with boolean
variables also known as partially ordered connectives. We consider
first-order formulae prefixed by partially ordered connectives,
denoted D, on finite structures. We characterize D as a fragment of
second-order existential logic Sigma-1-1-hearts whose formulae do not
allow for existential variables being argument of predicate
variables. We show that \Sigma-1-1-hearts harbors a strict hierarchy
induced by the arity of predicate variables and that it is not closed
under complementation, by means of a game-theoretical argument.
Admitting for at most one existential variable to appear as the
argument of a predicate variable already yields a logic coinciding
with full Sigma-1-1 , thus we show.
| Item Type: | Report |
|---|---|
| Report Nr: | PP-2006-31 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2006 |
| Uncontrolled Keywords: | Henkin quantifiers, finite model theory; NP vs. coNP; partially ordered connectives |
| Date Deposited: | 12 Oct 2016 14:36 |
| Last Modified: | 12 Oct 2016 14:36 |
| URI: | https://eprints.illc.uva.nl/id/eprint/206 |
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