Introduction

Abstract

Paul Erdős was always interested in infinity. One of his earliest results is an infinite analogue of (the then very recent) Menger’ s theorem (which was included in a classical book of his teacher Denes König). Two out of his earliest three combinatorial papers are devoted to infinite graphs. According to his personal recollections, Erdős always had an interest in “large cardinals” although his earliest work on this subject are joint papers with A. Tarski from the end of thirties. These interests evolved over the years into the Giant Triple Paper, with the Partition Calculus forming a field rightly called here Erdősian Set Theory.