A Power Function with a Fixed Finite Gap Everywhere

Journal of Symbolic Logic 72 (2):361 - 417 (2007)
  Copy   BIBTEX

Abstract

We give an application of the extender based Radin forcing to cardinal arithmetic. Assuming κ is a large enough cardinal we construct a model satisfying 2κ = κ⁺ⁿ together with 2λ = λ⁺ⁿ for each cardinal λ < κ, where 0 < n < ω. The cofinality of κ can be set arbitrarily or κ can remain inaccessible. When κ remains an inaccessible, Vκ is a model of ZFC satisfying 2λ = λ+n for all cardinals λ

Categories

Keywords

Reprint years

DOI

10.2178/jsl/1185803615

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,164

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Fixed point logics.Anuj Dawar & Yuri Gurevich - 2002 - Bulletin of Symbolic Logic 8 (1):65-88.
The expressive power of fixed-point logic with counting.Martin Otto - 1996 - Journal of Symbolic Logic 61 (1):147-176.
Counting finite models.Alan R. Woods - 1997 - Journal of Symbolic Logic 62 (3):925-949.
Yet another hierarchy theorem.Max Kubierschky - 2000 - Journal of Symbolic Logic 65 (2):627-640.
On the weak Kleene scheme in Kripke's theory of truth.James Cain & Zlatan Damnjanovic - 1991 - Journal of Symbolic Logic 56 (4):1452-1468.
Pseudo-finite homogeneity and saturation.Jörg Flum & Martin Ziegler - 1999 - Journal of Symbolic Logic 64 (4):1689-1699.
Rational choice on non-finite sets by means of expansion-contraction axioms.M. Carmen Sánchez - 1998 - Theory and Decision 45 (1):1-17.
À propos d'équations génériques.Frank O. Wagner - 1992 - Journal of Symbolic Logic 57 (2):548-554.
Function, modality, mental content.Bence Nanay - 2011 - Journal of Mind and Behavior 32 (2):84-87.
Finite Model Theory and its Applications.Erich Grädel, Phokion Kolaitis, Libkin G., Marx Leonid, Spencer Maarten, Vardi Joel, Y. Moshe, Yde Venema & Scott Weinstein - 2007 - Springer.
Generalizations of the Kruskal-Friedman theorems.L. Gordeev - 1990 - Journal of Symbolic Logic 55 (1):157-181.
Defining transcendentals in function fields.Jochen Koenigsmann - 2002 - Journal of Symbolic Logic 67 (3):947-956.
Axiom systems for first order logic with finitely many variables.James S. Johnson - 1973 - Journal of Symbolic Logic 38 (4):576-578.
Sharvy’s Lucy and Benjamin Puzzle.Thomas Forster - 2008 - Studia Logica 90 (2):249 - 256.

Analytics

Added to PP
2010-08-24

Downloads
18 (#777,769)

6 months
2 (#1,114,623)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Two‐cardinal diamond star.Pierre Matet - 2014 - Mathematical Logic Quarterly 60 (4-5):246-265.
Guessing more sets.Pierre Matet - 2015 - Annals of Pure and Applied Logic 166 (10):953-990.
A Laver-like indestructibility for hypermeasurable cardinals.Radek Honzik - 2019 - Archive for Mathematical Logic 58 (3-4):275-287.
Towers and clubs.Pierre Matet - 2021 - Archive for Mathematical Logic 60 (6):683-719.
Global singularization and the failure of SCH.Radek Honzik - 2010 - Annals of Pure and Applied Logic 161 (7):895-915.

View all 6 citations / Add more citations

References found in this work

Powers of regular cardinals.William B. Easton - 1970 - Annals of Mathematical Logic 1 (2):139.
Possible values for 2ℵn and 2ℵω.Moti Gitik & Carmi Merimovich - 1997 - Annals of Pure and Applied Logic 90 (1-3):193-241.
Possible values for 2 (aleph n) and 2 (aleph omega).Moti Gitik & Carmi Merimovich - 1997 - Annals of Pure and Applied Logic 90 (1-3):193-241.
Adding closed cofinal sequences to large cardinals.Lon Berk Radin - 1982 - Annals of Mathematical Logic 22 (3):243.

Add more references