- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Second-Order Characterizable Cardinals and Ordinals
Studia Logica 84 (3):425-449 (2006)
Abstract
The notions of finite and infinite second-order characterizability of cardinal and ordinal numbers are developed. Several known results for the case of finite characterizability are extended to infinite characterizability, and investigations of the second-order theory of ordinals lead to some observations about the Fraenkel-Carnap question for well-orders and about the relationship between ordinal characterizability and ordinal arithmetic. The broader significance of cardinal characterizability and the relationships between different notions of characterizability are also discussed.Author's Profile
Other Versions
No versions found
My notes
Similar books and articles
On second-order characterizability.T. Hyttinen, K. Kangas & J. Vaananen - 2013 - Logic Journal of the IGPL 21 (5):767-787.
On series of ordinals and combinatorics.James P. Jones, Hilbert Levitz & Warren D. Nichols - 1997 - Mathematical Logic Quarterly 43 (1):121-133.
Classical Logic is not Uniquely Characterizable.Isabella McAllister - 2022 - Journal of Philosophical Logic 51 (6):1345-1365.
The theorem of the means for cardinal and ordinal numbers.George Rousseau - 1993 - Mathematical Logic Quarterly 39 (1):279-286.
On the characterizability of the frames for the "unpreventability of the present and the past".Alberto Zanardo - 1986 - Notre Dame Journal of Formal Logic 27 (4):556-564.
Semantic and pragmatic characterizability of linguistic usage.Lennart Åqvist - 1967 - Synthese 17 (1):281 - 291.
Three characterizability problems in deontic logic.Lennart Åqvist - 2000 - Nordic Journal of Philosophical Logic 5 (2):65-82.
Are the Natural Numbers Fundamentally Ordinals?Bahram Assadian & Stefan Buijsman - 2018 - Philosophy and Phenomenological Research 99 (3):564-580.
Analytics
Added to PP
2009-01-28
Downloads
85 (#254,793)
6 months
3 (#1,061,821)
2009-01-28
Downloads
85 (#254,793)
6 months
3 (#1,061,821)
Historical graph of downloads
Author's Profile
Citations of this work
A General Setting for Dedekind's Axiomatization of the Positive Integers.George Weaver - 2011 - History and Philosophy of Logic 32 (4):375-398.
Fraenkel–Carnap Questions for Equivalence Relations.George Weaver & Irena Penev - 2011 - Australasian Journal of Logic 10:52-66.
References found in this work
Foundations without foundationalism: a case for second-order logic.Stewart Shapiro - 1991 - New York: Oxford University Press.
Completeness and Categoricity. Part I: Nineteenth-century Axiomatics to Twentieth-century Metalogic.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (1):1-30.
Completeness and categoricty, part II: 20th century metalogic to 21st century semantics.Steve Awodey & Erich H. Reck - 2002 - History and Philosophy of Logic 23 (1):77-92.
The Fraenkel‐Carnap question for Dedekind algebras.George Weaver & Benjamin George - 2003 - Mathematical Logic Quarterly 49 (1):92-96.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-99fc7d78b-s277s uwo