Switch to: References

Add citations

You must login to add citations.
  1. Large Cardinals, Inner Models, and Determinacy: An Introductory Overview.P. D. Welch - 2015 - Notre Dame Journal of Formal Logic 56 (1):213-242.
    The interaction between large cardinals, determinacy of two-person perfect information games, and inner model theory has been a singularly powerful driving force in modern set theory during the last three decades. For the outsider the intellectual excitement is often tempered by the somewhat daunting technicalities, and the seeming length of study needed to understand the flow of ideas. The purpose of this article is to try and give a short, albeit rather rough, guide to the broad lines of development.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Greatly Erdős cardinals with some generalizations to the Chang and Ramsey properties.I. Sharpe & P. D. Welch - 2011 - Annals of Pure and Applied Logic 162 (11):863-902.
    • We define a notion of order of indiscernibility type of a structure by analogy with Mitchell order on measures; we use this to define a hierarchy of strong axioms of infinity defined through normal filters, the α-weakly Erdős hierarchy. The filters in this hierarchy can be seen to be generated by sets of ordinals where these indiscernibility orders on structures dominate the canonical functions.• The limit axiom of this is that of greatly Erdős and we use it to calibrate (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   12 citations