 Mathematical game theory was founded in the early twentieth century. Although no mathematical links with logic emerged until the 1950s, it is striking how many of the early pioneers of game theory are also known for their contributions to logic: John Kemeny, J. C. C. McKinsey, John von Neumann, Willard Quine, Julia Robinson, Ernst Zermelo and others. In 1953 David Gale and Frank Stewart made fruitful connections between set theory and games. Shortly afterwards Leon Henkin suggested a way of using games to give semantics for infinitary languages.