How to define a linear order on finite models

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Abstract

We carry out a systematic investigation of the definability of linear order on classes of finite rigid structures. We obtain upper and lower bounds for the expressibility of linear order in various logics that have been studied extensively in finite model theory, such as least fixpoint logic LFP, partial fixpoint logic PFP, infinitary logic Lωω with a finite number of variables, as well as the closures of these logics under implicit definitions. Moreover, we show that the upper and lower bounds established here cannot be made substantially tighter, unless outstanding conjectures in complexity theory are resolved at the same time.

Keywords

Finite model theory
Computational complexity
Fixpoint logic
Infinitary logic
Implicit definability
Rigid models
Linear order
Graph isomorphism
Graph automorphism

MSC

03C13
03D15
68Q15

MSC

03C50
03C80

Cited by (0)

1

Partially supported by a grant from the University of Helsinki.

Partially supported by a 1993 John Simon Guggenheim Fellowship and by NSF Grants No. CCR-9108631, CCR-9307758, and INT-9024681.

2

Partially supported by a grant from the Emil Aaltonen Foundation.