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Some consequences are studied of Shavrukov's theorem regarding
the Magari algebras (diagonalizable algebras) that are embeddable in
the Magari algebra of formal arithmetical theories. Semantic charac
terizations of faithfully interpretable modal propositional theories in a
finite number of propo...
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Free Algebras Corresponding to Multiplicative Classical Linear Logic and
some Extensions.
Andreja Prijatelj
In this paper, constructions of free algebras corresponding to multiplicative
classical linear logic, its affine variant and their extensions with
ncontraction (n >= 2) are given. As a...
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The paper presents a settheoretic translation method for polymodal logics
that reduces the derivability problem of a large class of propositional
polymodal logics to the derivability problem of a very weak firstorder set
theory \Omega. Unlike most existing translation methods, the one we prop...
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Logics with the strong provability operator ``... is true and provable''
together with the proof operators ``p is a proof of...'' are axiomatized.
Kripkestyle completeness, decidability and arithmetical completeness of
these logics are established.
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On one decidable generalized quantifier logic corresponding to a decidable
fragment of firstorder logic
Natasha Alechina
Van Lambalgen (1990) proposed a translation from a language containing a
generalized quantifier Q into a firstorder language enriched with a family
of predicates R_i , ...
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An elementary construction of an ultrafilter on AlephOne
using the Axiom of Determinateness
Marco R. Vervoort
In this article we construct a free and scomplete ultrafilter on the set
\omega_1, using AD.
First we define for each V \subset \omega_1 a game G(V). From the axiom
AD we have that...
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We investigate modal deduction through translation into standard logic and set
theory. Derivability in the minimal modal logic is captured precisely by
translation into a weak, computationally attractive set theory \Omega. This
approach is shown equivalent to working with standard firstorder ...
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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...