Results 191 to 200 of about 789 (235)

Cardinal Characteristics on Large Cardinals

Fundamenta Mathematicae, 2021
Das Studium von Kardinalzahlcharakteristiken auf regul ren berabz hlbaren Kardinalzahlen hat in den letzten zehn Jahren erheblich an Popularit t gewonnen. Die Verallgemeinerungen des Cantor- und Baire-Raums auf regul re berabz hlbare Kardinalzahlen kappa induzieren auf nat rliche Weise Verallgemeinerungen der zugeh rigen ...
Friedman, Sy-David, Holy, Peter
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LARGE CARDINALS BEYOND CHOICE

The Bulletin of Symbolic Logic, 2019
AbstractThe HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V (in the sense that it correctly computes successors of singular cardinals greater than δ) or HOD is “far” from V (in the sense that all regular cardinals greater than or equal to δ are measurable in HOD).
Bagaria, Joan, Koellner, Peter, Woodin, W. Hugh   +2 more
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GENERICITY AND LARGE CARDINALS

Journal of Mathematical Logic, 2005
We lift Jensen's coding method into the context of Woodin cardinals. By a theorem of Woodin, any real which preserves a "strong witness" to Woodinness is set-generic. We show however that there are class-generic reals which are not set-generic but preserve Woodinness, using "weak witnesses".
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Are Large Cardinal Axioms Restrictive?

Philosophia Mathematica, 2023
AbstractThe independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim.
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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.
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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
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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.
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Weak Covering at Large Cardinals

Mathematical Logic Quarterly, 1997
AbstractWe show that weakly compact cardinals are the smallest large cardinals k where k+ < k+ is impossible provided 0# does not exist. We also show that if k+Kc < k+ for some k being weakly compact (where Kc is the countably complete core model below one strong cardinal), then there is a transitive set M with M ⊨ ZFC + “there is a strong ...
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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 ...
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Large cardinals and large dilators

Journal of Symbolic Logic, 1998
AbstractApplying Woodin's non-stationary tower notion of forcing, I prove that the existence of a supercompact cardinal κ in V and a Ramsey dilator in some small forcing extension V[G] implies the existence in V of a measurable dilator of size κ, measurable by κ-complete measures.
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