On Vopěnka’s Ultrafinitism

Abstrakt

It is perhaps unsurprising that the somewhat remote research area of ultrafinitism in the foundations of mathematics cautiously embraces the work of Petr Vopěnka on his Alternative Set Theory (AST) as a relevent effort. Membership in the “ultrafinitist club” is largely self-proclaimed, so one becomes an ultrafinitist by identifying as such, and Vopěnka’s writings present convincing membership evidence, although he might have shied away from the label. In his own words, in designing the AST he attempted to put forward a theory of natural infinity (in which task a sizeable group of coworkers was indispensable; a seminar on the AST was run in Prague for several years in the late 1970s).