Results 241 to 250 of about 1,581 (277)

Combinatorics on large cardinals

Journal of Symbolic Logic, 1992
Our framework is ZFC, and we view cardinals as initial ordinals. Baumgartner ([Bal] and [Ba2]) studied properties of large cardinals by considering these properties as properties of normal ideals and not as properties of cardinals alone. In this paper we study these combinatorial properties by defining operations which take as input one or more ideals ...
openaire   +2 more sources

Inner Models and Large Cardinals

Bulletin of Symbolic Logic, 1995
In this paper, we sketch the development of two important themes of modern set theory, both of which can be regarded as growing out of work of Kurt Gödel. We begin with a review of some basic
openaire   +1 more source

On large cardinals and partition relations

Journal of Symbolic Logic, 1971
A significant portion of the study of large cardinals in set theory centers around the concept of “partition relation”. To best capture the basic idea here, we introduce the following notation: for x and y sets, κ an infinite cardinal, and γ an ordinal less than κ, we let [x]γ denote the collection of subsets of x of order-type γ and abbreviate with ...
E. M. Kleinberg, Richard A. Shore
openaire   +2 more sources

Intensionality, Reflection, and Large Cardinals

Siberian Mathematical Journal, 2002
The authors study some axiomatic systems of set theory in which the reflection principle is postulated for all formulas without class quantifiers. These systems are interesting because in some of them the existence of large cardinals can be proven. Some aspects of interpretability of these theories in classical systems and in each other are considered.
Belyakin, N. V., Ganov, V. A.
openaire   +2 more sources

Large cardinals and projective sets

Archive for Mathematical Logic, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haim Judah, Otmar Spinas
openaire   +2 more sources

Large cardinals at the brink

Annals of Pure and Applied Logic
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

On the ordering of certain large cardinals

Journal of Symbolic Logic, 1979
It is well known that the first strongly inaccessible cardinal is strictly less than the first weakly compact cardinal which in turn is strictly less than the first Ramsey cardinal, etc. However, once one passes the first measurable cardinal the inequalities are no longer strict.
openaire   +1 more source

Large Cardinal Properties of Small Cardinals

1998
The fact that small cardinals (for example N1 and N2) can consistently have properties similar to those of large cardinals (for example measurable or supercompact cardinals) is a recurring theme in set theory. In these notes I discuss three examples of this phenomenon; stationary reflection, saturated ideals and the tree property.
openaire   +1 more source

Sequentially Large Cardinals

1983
Publisher Summary This chapter discusses sequentially large cardinals. Large cardinals defined via elementary embeddings are the largest cardinals and the strongest in terms of relative consistency strength. The chapter defines the sequentially large cardinals are defined, a spectrum of large cardinals that are defined via elementary embeddings, in ...
openaire   +1 more source

Tall Cardinals in Extender Models

Notre Dame Journal of Formal Logic, 2021
Ralf Schindler
exaly