The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and… Expand

This is the expository paper on strong axioms of infinity and elementary embeddings origi;,ally to have been authored by Reinhardt and Solovay. It has been owed for some time and already cited with… Expand

This paper considers a simple finite corollary of a theorem of infinite combinatorics of Erdos and Rado and shows it to be independent of Peano Arithmetic and provides a treatment of the proof whose organization and brevity make it suitable for expository purposes.Expand

ion and general ideas.” Compare Meinong, Über Möglichkeit und Wahrscheinlichkeit, p. 178: “Besonders geeignet sind vielmehr Begriffsgegenstände, wie uns deren etwa durch Definitionen gegeben werden.… Expand

For a filter over a regular cardinal, least functions and the consequent notion of weak normality are described. The following two results, which make a basic connection between the existence of… Expand

Handbook of Set Theory, Volume I, Akihiro Kanamori, 0. Introduction Thomas Jech, 1. Stationary Sets Andras Hajnal and Jean Larson, 2. Partition Relations Stevo Todorcevic, 3. Coherent Sequences Greg… Expand

An account of the development of set theory from its beginnings through the creation of forcing based on contentions, with an avowedly Whiggish emphasis on the heritage that has been retained and developed by current set theory.Expand