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We prove that a Spector-like ultrapower extension N of a countable Solovay
model M (where all sets of reals are Lebesgue measurable) is equal to the set
of all sets constructible from reals in a generic extension M[\alpha] where
\alpha is a random real over M. The proof involves an almost everyw...
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We show how sequent calculi for some generalized quantifiers can be
obtained by generalizing the Herbrand approach to ordinary first order
proof theory. Typical of the Herbrand approach, as compared to plain se
quent calculus, is increased control over relations of dependence between
variables. ...
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In this paper, we develop various aspects of the finite model theory of
propositional modal logic. In particular, we show that certain results
about the expressive power of modal logic over the class of all structures,
due to van Benthem and his collaborators, remain true over the class of
fi...
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In this paper, we will give a short survey of results on decision problems
and the finite model property of substructural logics. The paper is far from
a complete list of these results, since a lot of results have been obtained
already in some restricted classes of substructural logics, like r...
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We present some algebraic tools and apply them to the study of the expressive
power of bounded formulas in secondorder arithmetic. The accent is on negative
results. The techniques studied here come from Boolean circuit complexity and
are adapted to the context of arithmetic. One of the purposes...
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