Universes in explicit mathematics

Universes in explicit mathematics

This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman’s T0.

The Quantiication Operator in Explicit Mathematics with Universes and Iterated Xed Point Theories with Ordinals

This paper is about two topics: 1. systems of explicit mathematics with universes and a non-constructive quantiication operator ; 2. iterated xed point theories with ordinals. We give a proof-theoretic treatment of both families of theories; in particular, ordinal theories are used to get upper bounds for explicit theories with nitely many universes.

Impredicative Overloading in Explicit Mathematics

We introduce the system OTN of explicit mathematics based on elementary separation, products, joins and weak power types. In this theory, we will define late-bound overloaded functions with a corresponding impredicative type structure à la λ&. Then we present a set-theoretic model for OTN which provides a denotational semantics for impredicative overloading without restricting itself to early-b...

Explicit mathematics: W-type, models

Applicative Theories and Explicit Mathematics

[5] Solomon Feferman and Gerhard Jäger. Systems of explicit mathematics with non-constructive µ-operator. [6] Solomon Feferman and Gerhard Jäger. Systems of explicit mathematics with non-constructive µ-operator. [9] Susumu Hayashi and Satoshi Kobayashi. A new formulation of Feferman's system of functions and classes and its relation to Frege structures.