Generalized ordinal notation.

A comparison of well-known ordinal notation systems for epsilon0

We consider five ordinal notation systems of ε0 which are all well-known and of interest in proof-theoretic analysis of Peano arithmetic: Cantor’s system, systems based on binary trees and on countable tree-ordinals, and the systems due to Schütte and Simpson, and to Beklemishev. The main point of this paper is to demonstrate that the systems except the system based on binary trees are equivale...

Generalized ordinal sums and translations

We extend the lattice embedding of the axiomatic extensions of the positive fragment of intuitionistic logic into the axiomatic extensions of intuitionistic logic to the setting of substructural logics. Our approach is algebraic and uses residuated lattices, the algebraic models for substructural logics. We generalize the notion of the ordinal sum of two residuated lattices and use it to obtain...

Generalized Odds Ratios for Ordinal Data

Iteration templates as generalized ordinal notations

This document is a survey of the four papers [λH], [Sch], [Com], [FandH]. It gives the relevant background and shows how the papers fit together to form a whole. Material from those papers is repeated only when necessary. As it stands the document is not intended for publication. However, if there is sufficient interest then I may rewrite it to include [λH], [Sch], [Com], [FandH] and so form a ...

A comparison of well - known ordinal notation systems for ε 0

We consider five ordinal notation systems of ε0 which are all well-known and of interest in proof-theoretic analysis of Peano arithmetic: Cantor’s system, systems based on binary trees and on countable tree-ordinals, and the systems due to SchütteSimpson and Beklemishev. The main point of this paper is to demonstrate that the systems except the system based on binary trees are equivalent as str...