Raphael M. Robinson: Difference between revisions

Robinson worked on [[mathematical logic]], [[set theory]], [[geometry]], [[number theory]], and [[combinatorics]]. In 1937 he set out a simpler and more conventional version of the [[John von Neumann]] 1923 [[Von Neumann–Bernays–Gödel set theory|axiomatic set theory]]. Soon after [[Alfred Tarski]] joined Berkeley's mathematics department in 1942, Robinson began to do major work on the [[foundations of mathematics]], building on Tarski's concept of [[Decidability (logic)#Decidability of a theory|essential undecidabilility]], by proving a number of mathematical theories [[decision problem|undecidable]]. In 1950 Robinson proved that an essentially undecidable theory need not have an infinite number of [[axiom]]s by coming up with a counterexample: [[Robinson arithmetic Q|Robinson arithmetic ''Q'']]. ''Q'' is finitely axiomatizable because it lacks [[Peano arithmetic]]'s axiom schema of [[mathematical induction|induction]]; nevertheless ''Q'', like Peano arithmetic, is [[Gödel's Incompleteness Theorem|incomplete]] and undecidable in the sense of [[Kurt Gödel|Gödel]]. Robinson's work on undecidability culminated in his coauthoring Tarski et al. (1953), which established, among other things, the undecidability of [[group theory]], [[lattice theory]], abstract [[projective geometry]], and [[closure algebra]]s.