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The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general...
We study lowness for genericity. We show that there exists no Turing degree which is low for 1-genericity and all of computably traceable degrees are low for weak 1-genericity.
The non-commutative counterpart of the well-known Łukasiewicz propositional logic is developed, in strong connection with the algebraic theory of psMV-algebras. An extension by a new unary logical connective is also considered and a stronger completeness result is proved for this system.
A new set of conversions for derivations in the system of sequents for intuitionistic predicate logic will be defined. These conversions will be some modifications of Zucker's conversions from the system of sequents [InlineMediaObject not available: see fulltext.] from , which will have the...
Simpson introduced the lattice [InlineMediaObject not available: see fulltext.] of Π0
1 classes under Medvedev reducibility. Questions regarding completeness in [InlineMediaObject not available: see fulltext.] are related to questions about measure and randomness. We present a solution to a...
We prove that the existential theory of the Turing degrees, in the language with Turing reduction, 0, and unary relations for the classes in the generalized high/low hierarchy, is decidable.
A=(A,0,¬,⊕) is an abelian monoid (A,0,⊕) equipped with a unary operation ¬ such that ¬¬x=x,x⊕¬0=¬0, and y⊕¬(y⊕¬x)=x⊕¬(x⊕¬y). Chang proved that the equational class of MV-algebras is generated by the real unit interval [0,1] equipped with the operations ¬x=1−x and x⊕y=min(1,x+y)....
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