If [Formula: see text] is regular and text], then the existence of a weakly presaturated ideal on implies text]. This partially answers question Foreman Magidor about approachability As corollary, we show that if there such semiproper, CH holds. We also some barriers to getting tree property saturated simultaneously successor cardinal from conventional forcing methods.

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [25]. It investigates topological notions defined by means of  -open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying opera...

1. An O(mm(n) log(n)) = O(nω+ ) algorithm which finds the shortest distance matrix for a graph G by recursively finding the shortest distance matrix for the graph G2. 2. The problem of determining the successor matrix for tripartite graphs. 3. O(nω) time algorithm for finding successor matrix in in a simple tripartite graph when there is a unique successor for any 2 vertices. 4. An O(mm(n) log(...

We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the second. These problems are c...

We provide upper and lower bounds in consistency strength for the theories “ZF + ¬ACω + All successor cardinals except successors of uncountable limit cardinals are regular + Every uncountable limit cardinal is singular + The successor of every uncountable limit cardinal is singular of cofinality ω” and “ZF + ¬ACω + All successor cardinals except successors of uncountable limit cardinals are re...

One of the fundamental results of finite model theory is Immerman’s characterization [10,11] of the complexity class NL (non-deterministic logspace) as the class of problems definable in transitive closure logic augmented with a built-in successor relation, (±TC)∗[FOs]. Essentially, by “built-in successor relation” we mean that any sentence of the logic has access to a successor relation on the...