Erratum to: Epimorphisms Between Linear Orders

Epimorphisms Between Linear Orders

We study the relation on linear orders induced by order preserving surjections. In particular we show that its restriction to countable orders is a bqo.

Extending Partial Orders to Dense Linear Orders

Epimorphisms between 2–bridge link groups

We give a systematic construction of epimorphisms between 2–bridge link groups. Moreover, we show that 2–bridge links having such an epimorphism between their link groups are related by a map between the ambient spaces which only have a certain specific kind of singularity. We show applications of these epimorphisms to the character varieties for 2–bridge links and π1 –dominating maps among 3–m...

Elementary epimorphisms between models of set theory

We show that every Π1-elementary epimorphism between models of ZF is an isomorphism. On the other hand, nonisomorphic Σ1-elementary epimorphisms between models of ZF can be constructed, as can fully elementary epimorphisms between models of ZFC−. Elementary epimorphisms were introduced by Philipp Rothmaler in [Rot05]. A surjective homomorphism f : M → N between two model-theoretic structures is...

Reflecting Linear Arithmetic: From Dense Linear Orders to Presburger Arithmetic

This talk presents reflected quantifier elimination procedures for both integer and real linear arithmetic. Reflection means that the algorithms are expressed as recursive functions on recursive data types inside some logic (in our case HOL), are verified in that logic, and can then be applied to the logic itself. After a brief overview of reflection we will discuss a number of quantifier elimi...