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Several investigations in probability theory and the theory of expert systems show that it is important to search for some reasonable generalizations of fuzzy logics (e.g. Łukasiewicz, Gödel or product logic) having a non-associative conjunction. In the present paper, we offer a non-associative...
We introduce the simpler and shorter proof of Hajek’s theorem that the mathematical induction on
ω implies a contradiction in the set theory with the comprehension principle within Łukasiewicz predicate logic Ł
(Hajek Arch Math Logic 44(6):763–782, 2005) by extending the proof in...
We show that a version of Ramsey’s theorem for trees for arbitrary exponents is equivalent to the subsystem
of reverse mathematics.
We show that a theory of autonomous iterated Ramseyness based on second order arithmetic (SOA) is proof-theoretically equivalent to
-comprehension. The property of Ramsey is defined as follows. Let X be a set of real numbers, i.e. a set of infinite sets of natural numbers. We call...
We introduce a new approach to the model theory of metric structures by defining the notion of a metric abstract elementary class (MAEC) closely resembling the notion of an abstract elementary class. Further we define the framework of a homogeneous MAEC were we additionally assume the existence...
denote the Stone–Čech compactification of the set
of natural numbers (with the discrete topology), and let
denote the remainder
. We show that, interpreting modal diamond as the closure in...
It is known that the box dimension of any Martin-Löf random closed set of
. Barmpalias et al. [J Logic Comput 17(6):1041–1062, 2007] gave one method of producing such random closed sets and then computed the box dimension, and posed several...
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