A new construction of non-constructible subset of ω
A new decidable Horn fragment of predicate calculus.
A new definition of the fuzzy set
The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.
A new large cardinal and Laver sequences for extendibles
We define a new large cardinal axiom that fits between and in the hierarchy of axioms described in [SRK]. We use this new axiom to obtain a Laver sequence for extendible cardinals, improving the known large cardinal upper bound for the existence of such sequences.
A new proof of a theorem of Balcerzyk, Białynicki-Birula and Łoś
A new proof of James' sup theorem.
We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson: "If a normed space E does not contain any asymptotically isometric copy of l1, then every bounded sequence of E' has a normalized l1-block sequence pointwise converging to 0".
A new proof of Kelley's Theorem
Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.
A new Proof of Prešić's Theorem on Finite Equations
A new proof of Reiterman's theorem
A new type assignment for ...-terms.
A new type of affine Borel function.
A non commutative generalization of -autonomous lattices
Pseudo -autonomous lattices are non-commutative generalizations of -autonomous lattices. It is proved that the class of pseudo -autonomous lattices is a variety of algebras which is term equivalent to the class of dualizing residuated lattices. It is shown that the kernels of congruences of pseudo -autonomous lattices can be described as their normal ideals.
A non-associative generalization of MV-algebras
A non-special -tree with special -subtrees
A nonstandard approach to arithmetic.
A nonstandard approach to fuzzy set theory
A non-standard approach to the Euclidean study of plane curves.
A Nonstandard Approach to the Uniqueness Problem for the Navier-Stokes Equations.
A non-Standard Characterization of the norm of free Ultrafilters
A nonstandard set theory