PP-2006-31:
Sevenster, Merlijn and Tulenheimo, Tero
(2006)
*Partially ordered connectives and Sigma-1-1 on finite models.*
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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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