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We study the preservation of the property of [InlineMediaObject not available: see fulltext.] being a Solovay model under proper projective forcing extensions. We show that every [InlineMediaObject not available: see fulltext.] strongly-proper forcing notion preserves this property. This yields...
Formulas of n variables of Łukasiewicz sentential calculus can be represented, via McNaughton’s theorem, by piecewise linear functions, with integer coefficients, from hypercube [0,1]
to [0,1], called McNaughton functions. As a consequence of the McNaughton representation of a formula it is...
We show that every MALL proof-structure  satisfies the property of softness, originally a categorical notion introduced by Joyal. Furthermore, we show that the notion of hereditary softness precisely captures Girard’s algebraic restriction of the technical condition on proof-structures....
The powerset operator, [InlineMediaObject not available: see fulltext.], is an operator which (1) sends sets to sets,(2) is defined by a positive formula and (3) raises the cardinality of its argument, i.e., |[InlineMediaObject not available: see fulltext.](x)|>|x|. As a consequence of (3),...
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