Paul Gorbow

University of Gothenburg | GU · Department of Philosophy, Linguistics and Theory of Science

This thesis concerns embeddings and self-embeddings of foundational structures in both set theory and category theory. The first part of the work on models of set theory consists in establishing a refined version of Friedman's theorem on the existence of embeddings between countable non-standard models of a fragment of ZF, and an analogue of a theo...

New Foundations ($\mathrm{NF}$) is a set theory obtained from naive set theory by putting a stratification constraint on the comprehension schema; for example, it proves that there is a universal set $V$. $\mathrm{NFU}$ ($\mathrm{NF}$ with atoms) is known to be consistent through its close connection with models of conventional set theory that admi...

The foundations of category theory has been a source of many perplexities ever since the groundbreaking 1945-introduction of the subject by Eilenberg and Mac Lane; e.g., how is one to avoid Russell-like paradoxes and yet have access to objects that motivate the study in the �first place, such as the category of all groups, or the category of all to...

Abstract We take a tour through,some,uses of independence,in stability theory. The unifying theme is infinite sequences. In particular, we develop the basic theory of independent sequences, Morley sequences, indiscernible sequences, Shelah trees, F-isolation and stationary sets. The essay ends with a proof that a stable but not superstable,theory h...