The heart of the extended rough set theory is the generalization of the notion of the standard set inclusion degree. Considering the equivalent relationship between equivalence class in rough set theory and concept in concept lattice, we will study a classification problem of undefinable object set (undefinable object set is the object set that is not an extension) in concept lattice. First, wi...

Small independent edge dominating sets in graphs of maximum degree three – p. 1/34

Let d be a Turing degree, R[d] and Q[d] denote respectively classes of recursively enumerable (r.e.) and all degrees in which d is relatively enumerable. We proved in [ta] that there is a degree d containing differences of r.e.sets (briefly, d.r.e.degree) such that R[d] possess a least element m>0. Now we show the existence of a d.r.e. d such that R[d] has no a least element. We prove also that...

Alon, Kleitman, Lipton, Meshulam, Rabin and Spencer (Graphs. Combin. 7 (1991), no. 2, 97-99) proved, that for any hypergraph F = fF1; F2; : : : ; Fd(q 1)+1g, where q is a primepower, and d denotes the maximal degree of the hypergraph, there exists an F0 F , such that jSF2F0 F j 0 (mod q). We give a direct, alternative proof for this theorem, and we also give an explicit construction of a hyperg...

This paper is concerned with the construction of intervals of computably enumerable degrees in which the lattice M5 (see Figure 1) cannot be embedded. Actually, we construct intervals I of computably enumerable degrees without any weak critical triples (this implies that M5 cannot be embedded in I, see Section 2). Our strongest result is that there is a low2 computably enumerable degree e such ...

It is investigated how much information of a random set can be preserved if one splits the random set into two halves or, more generally, cuts out an infinite portion with an infinite recursive set. The two main results are the following ones: 1. Every high Turing degree contains a Schnorr random set Z such that Z ≡T Z ∩ R for every infinite recursive set R. 2. For each set X there is a Martin-...

It is shown that a set is low for weakly 1-generic iff it has neither dnr nor hyperimmune Turing degree. As this notion is more general than being recursively traceable, this answers negatively a recent question on the characterization of these sets. Furthermore, it is shown that every set which is low for weakly 1-generic is also low for Kurtz-random. In addition to this, it is shown that a se...

Recently a tendency has arisen in cultural criticism to reactivate the notion of hybridity as a way to open a new path for the rethinking of resistance and dominance. However, by conceptualizing hybridity as a timeless form of oppositionality, this new critical direction has tended to succumb to the temptation of homogenizing multiple realities. Through a comparison of the urban forms of Vancou...