We study the lter L (A) of computably enumerable supersets (modulo nite sets) of an r-maximal set A and show that, for some such set A, the property of being co nite in L (A) is still 0 3 -complete. This implies that for this A, there is no uniformly computably enumerable \tower" of sets exhausting exactly the coin nite sets in L (A).

the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...

The creative sets of Post [4] are the recursively enumerable sets whose complements are productive in the sense of Dekker [l]. In [l], Dekker introduces the class of semiproductive sets, which properly includes the class of productive sets. If we define a set to be semicreative if it is recursively enumerable and has a semiproductive complement, we obtain a natural generalization of creative se...

We proposed the theory of multi-fuzzy sets [Sabu and Ramakrishnan (2010a), (2011a)] as an extension of theories of fuzzy sets, L-fuzzy sets [Goguen (1967)] and intuitionistic fuzzy sets [Atanassov (1986)]. Theory of multi-fuzzy sets deals with multi-level fuzziness and multi-dimensional fuzziness. Our previous papers discussed the basic notions of multi-fuzzy sets, multi-fuzzy topology, and mul...

D. Molodtsov (1999) introduced the concept of a soft set as a new approach for modeling uncertainties. The aim of this work is to define special kinds of soft sets, namely soft, L-fuzzifying soft, L-soft, and L-fuzzy soft neighborhood sets and to use them in order to give an alternative characterization of categories related to topology: crisp topological, L-topological, L-fuzzifying topologica...

We prove that the class NP has Co-NP-immune sets relative to a random oracle. Moreover, we prove that, relative to a random oracle, there are L 2 P and NP-set L 1 L such that L 1 is Co-NP-immune and L n L 1 is NP-immune. The second theorem implies the theorem in 4] that Co-NP has NP-immune sets relative to a random oracle.

In this paper, let P l n;≤s;k denote a set of k-flaw preference sets (a1, . . . , an) with n parking spaces satisfying that 1 ≤ ai ≤ s for any i and a1 = l and p l n;≤s;k = |P l n;≤s;k|. We use a combinatorial approach to the enumeration of k-flaw preference sets by their leading terms. The approach relies on bijections between the k-flaw preference sets and labeled rooted forests. Some bijecti...

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...

This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of L-computable functions (computable Lebesgue integrable functions) with a size notion, by introducing L-computable Baire categories. We show that L-computable Baire categories satisfy the following three basic properties. Singleton sets {f} (where f is L-computable) ar...

This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of L-computable functions (computable Lebesgue integrable functions) with a size notion, by introducing L-computable Baire categories. We show that L-computable Baire categories satisfy the following three basic properties. Singleton sets {f} (where f is L-computable) ar...