Game, Set, Brexit!

Two Game-Set Inequalities

Two players compete in a contest where the first player to win a specified number of points wins the game, and the first player to win a specified number of games wins the set. This paper proves two generalized inequalities, each independent of the probability of winning a point, concerning the better player’s chances of winning. Counterexamples are given for two additional conjectured inequali...

Brexit and health services.

On the set coincidence game

In the Set Coincidence Game G(V, W), two players alternately choose elements not previously chosen from a finite, nonempty set V, and W is a given family of nonempty subsets of V (the ‘winning sets’). The winner is that player who first adds an element to the set of ‘chosen’ elements 5, so that S E W. This game is closely related to and generalizes Ringeisen’s Isolation Game on graphs. We devel...

The stationary set splitting game

The stationary set splitting game is a game of perfect information of length ω1 between two players, unsplit and split, in which unsplit chooses stationarily many countable ordinals and split tries to continuously divide them into two stationary pieces. We show that it is possible in ZFC to force a winning strategy for either player, or for neither. This gives a new counterexample to Σ2 maximal...

Brexit and Translational Research

In a historic referendum on June 23, 2016, the UK voted to leave the European Union (EU) after more than four decades of membership. For the time being, the UK is still a member of the EU until the UK government triggers Article 50 of the Lisbon Treaty–which probably won't happen before the end of 2016. A minimum of 2 years of negotiations will follow before theUK ceases to be an EUmember. This...