A vertex set D in graph G is called a geodetic set if all vertices of G are lying on some shortest u–v path of G, where u, v 2 D. The geodetic number of a graph G is the minimum cardinality among all geodetic sets. A subset S of a geodetic set D is called a forcing subset of D if D is the unique geodetic set containing S. The forcing geodetic number of D is the minimum cardinality of a forcing ...

A certain approach to paraconsistency was initiated by works of R. Jennings and P. Schotch. In their “Inference and necessity” [4] they proposed a notion of a level of inconsistency (incoherence) of a given set of premises. This level is a measure that assigns to a given set of premises X, the least number of elements of covers of X that consist of consistent subsets of X. The idea of the level...

In the paper we probe the possibilities of creating a Kurepa tree in a generic extension of a model of CH plus no Kurepa trees by an ω1-preserving forcing notion of size at most ω1. In the first section we show that in the Lévy model obtained by collapsing all cardinals between ω1 and a strongly inaccessible cardinal by forcing with a countable support Lévy collapsing order many ω1preserving fo...