Separating principles below

Separating principles below Ramsey’s Theorem for Pairs

In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT22, Ramsey’s Theorem for Pairs. These principles tend to fall outside of the “big five” systems of reverse mathematics and a complicated picture of subsystems below RT22 has emerged. In this paper, we answer two open questions concerning these s...

Separating weak partial square principles

We introduce the weak partial square principles pλ,κ and p λ,<κ, which combine the ideas of a weak square sequence and a partial square sequence. We construct models in which weak partial square principles fail. The main result of the paper is that λ,κ does not imply λ,<κ. Let λ be a regular uncountable cardinal and let κ ≤ λ be a nonzero cardinal. Recall the square principle λ,κ (respectively ...

Pmax VARIATIONS FOR SEPARATING CLUB GUESSING PRINCIPLES

In his book on Pmax [6], Woodin presents a collection of partial orders whose extensions satisfy strong club guessing principles on ω1. In this paper we employ one of the techniques from this book to produce Pmax variations which separate various club guessing principles. The principle (+) and its variants are weak guessing principles which were first considered by the second author [3] while s...

Separating universal principles from attrition and transfer in heritage language

Salvage of a Below Knee Amputation Utilizing Rotationplasty Principles in a Patient with Chronic Tibial Osteomyelitis

INTRODUCTION Chronic osteomyelitis is a disease that requires fastidious treatment to eliminate. However, when eradication is unable to be achieved through exhaustive modalities of antibiotic therapy and multiple debridements, significant resection of the infected bone and soft tissue must be considered, including amputation. Here we report of a salvage procedure for chronic osteomyelitis of th...