Assuming that every set is constructible, we find a Π1 maximal cofinitary group of permutations of N which is indestructible by Cohen forcing. Thus we show that the existence of such groups is consistent with arbitrarily large continuum. Our method also gives a new proof, inspired by the forcing method, of Kastermans’ result that there exists a Π1 maximal cofinitary group in L.

Let G be a connected graph of order p and let 0 ::f. s ~ V ( G). Then S is a rad(G)-forcing set (or a radius-forcing set of G) if, for each v E V(G), there exists v' E S with dc(v, v') ?: rad(G). The cardinality of a smallest radius-forcing set of G is called the radius-forcing number of G and is denoted by rf(G). A graph G is called a randomly k-forcing graph for a positive integer k if every ...

Gentner and Rautenbach conjectured that the size of a minimum zero forcing set in a connected graph on n vertices with maximum degree 3 is at most 1 3 n + 2. We disprove this conjecture by constructing a collection of connected graphs {Gn} with maximum degree 3 on arbitrarily large number of vertices, having zero forcing number at least 4 9 |Gn|.

We present a new forcing notion combining diagonal supercompact Prikry focing with interleaved extender based forcing. We start with a supercompact cardinal κ. In the final model the cofinality of κ is ω, the singular cardinal hypothesis fails at κ and GCH holds below κ. Moreover we define a scale at κ, which has a stationary set of bad points in the ground model.

With each of the classical tree-like forcings adjoining a new real, one can associate a σ-ideal on the reals in a natural way. For example, the ideal s0 of Marczewski null sets corresponds to Sacks forcing S, while the ideal r0 of nowhere Ramsey sets corresponds to Mathias forcing R. We show (in ZFC) that none of these ideals is included in any of the others. We also discuss Mycielski’s ideal P...

The anti-oxidant activities for a diverse set of flavonoids as TEAC (Trolox equivalent anti-oxidant capacity), assay were subjected to 3D-QSAR (3 dimensional quantitative structural-activity relationship) studies using CoMFA (comparative molecular field analysis) and CoMSIA (comparative molecular similarity indices analysis). The obtained results indicated superiority of CoMSIA model over CoMFA...

Mathematicians are one over on the physicists in that they already have a unified theory of mathematics, namely set theory. Unfortunately the plethora of independence results since the invention of forcing has taken away some of the luster of set theory in the eyes of many mathematicians. Will man's knowledge of mathematical truth be forever limited to those theorems derivable from the standard...

One of the basic concepts of set theoretic geology is the mantle of a model of set theory V: it is the intersection of all grounds of V, that is, of all inner models M of V such that V is a set-forcing extension of M . The main theme of the present paper is to identify situations in which the mantle turns out to be a fine structural extender model. The first main result is that this is the case...

Zero forcing is a combinatorial game played on a graph with a goal of changing the color of every vertex at minimal cost. This leads to a parameter known as the zero forcing number that can be used to give an upper bound for the maximum nullity of a matrix associated with the graph. A variation on the zero forcing game is introduced that can be used to give an upper bound for the maximum nullit...