4 citations · 13 across the 13 of their papers we have counts for
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Dependence and Independence
Erich Grädel, Jouko Väänänen
We introduce an atomic formula intuitively saying that given variables are independent from given other variables if a third set of variables is kept constant. We contrast this wit…
On Second-order Characterizability
Tapani Hyttinen, Kaisa Kangas, Jouko Väänänen
We investigate the extent of second order characterizable structures by extending Shelah's Main Gap dichotomy to second order logic. For this end we consider a countable complete f…
The size of a formula as a measure of complexity
Lauri Hella, Jouko Väänänen
We introduce a refinement of the usual Ehrenfeucht-Fra\"ıssé game. The new game will help us make finer distinctions than the traditional one. In particular, it can be used to meas…
Axiomatizing first order consequences in dependence logic
Juha Kontinen, Jouko Väänänen
Dependence logic, introduced in [8], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this…