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The concept of a generalized quantiier of a given similarity type was deened in Lin66]. Our main result says that on nite structures diierent similarity types give rise to diierent classes of generalized quantiiers. More exactly, for every similarity type t there is a generalized quantiier of type t which is not deenable in the extension of rst order logic… (More)

This work presents a classification of weak models of distributed computing. We focus on deterministic distributed algorithms, and we study models of computing that are weaker versions of the widely-studied port-numbering model. In the port-numbering model, a node of degree <i>d</i> receives messages through <i>d</i> input ports and it sends messages… (More)

We introduce a new framework for classifying logics on finite structures and studying their expressive power. This framework is based on the concept of almost everywhere equivalence of logics, that is to say, two logics having the same expressive power on a class of asymptotic measure 1. More precisely, if L, L 0 are two logics and is an asymptotic measure… (More)

We study the expressive power of various modal logics with team semantics. We show that exactly the properties of teams that are downward closed and closed under team k-bisimulation, for some finite k, are definable in modal logic extended with intu-itionistic disjunction. Furthermore, we show that the expressive power of modal logic with intuitionistic… (More)

We carry out a systematic investigation of the deenability of linear order on classes of nite rigid structures. We obtain upper and lower bounds for the expressibility of linear order in various logics that have been studied extensively in nite model theory, such as least xpoint logic LFP, partial xpoint logic PFP, innnitary logic L ! 1! with a nite number… (More)

- Ari Koponen, Kerkko Luosto
- 2000

We consider logical deenability of the group-theoretic notions of simplicity, nilpotency and solvability on the class of nite groups. On one hand, we show that these notions are deenable by sentences of deterministic transitive closure logic DTC. These results are based on known group-theoretic results. On the other hand, we prove that simplicity,… (More)

A combinatorial criterium is given when a monadic quantiier is expressible by means of universe-independent monadic quantiiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the HH artig quantiier is not deenable by monadic quantiiers. The… (More)