# On the permissibility of impredicative comprehension

**Date**: Tuesday 7 February 2017, 16:30 – 18:00**Location**: Mathematics Level 8, MALL 1 & 2, School of Mathematics**Type**: Logic, Seminars, Pure Mathematics**Cost**: Free

#### Øystein Linnebo, University of Oslo. Part of the logic seminar series.

Which comprehension axioms of higher-order logic are acceptable? It is well known that unrestricted higher-order comprehension is incompatible with unrestricted reification of higher-order entities. In search of a response to this conflict, an argument against all forms of impredicative comprehension is formulated. Although the argument is ultimately rejected, a careful analysis of it points the way to some milder logical restrictions, which suffice to resolve the conflict.

**Øystein Linnebo**, *University of Oslo*