In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 3-26 (2019)

Authors
Džamonja Mirna
University of East Anglia
Abstract
The status of independent statements is the main problem in the philosophy of set theory. We address this problem by presenting the perspective of a practising set theorist. We thus give an authentic insight in the current state of thinking in set-theoretic practice, which is to a large extent determined by independence results. During several meetings, the second author asked the first author about the development of forcing, the use of new axioms and set-theoretic intuition on independence. Parts of these conversations are directly presented in this article. They are supplemented by important mathematical results as well as discussion sections. Finally, we present three hypotheses about set-theoretic practice: First, that most set theorists were surprised by the introduction of the forcing method. Second, that most set theorists think that forcing is a natural part of contemporary set theory. Third, that most set theorists prefer an answer to a problem with the help of a new axiom of lowest possible consistency strength, and that for most set theorists, a difference in consistency strength weighs much more than the difference between Forcing Axiom and Large Cardinal Axiom.
Keywords Set-theoretic practice  Forcing  Interviews
Categories (categorize this paper)
Buy the book Find it on Amazon.com
DOI 10.1007/978-3-030-15655-8_1
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 72,564
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

The Price of Mathematical Scepticism.Paul Blain Levy - forthcoming - Philosophia Mathematica.

Add more citations

Similar books and articles

Interview With a Set Theorist.Deborah Kant & Mirna Džamonja - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics. Springer Verlag. pp. 3-26.
Distributive Proper Forcing Axiom and Cardinal Invariants.Huiling Zhu - 2013 - Archive for Mathematical Logic 52 (5-6):497-506.
A Maximal Bounded Forcing Axiom.David Asperó - 2002 - Journal of Symbolic Logic 67 (1):130-142.
Forcing Indestructibility of Set-Theoretic Axioms.Bernhard König - 2007 - Journal of Symbolic Logic 72 (1):349 - 360.
Removing Laver Functions From Supercompactness Arguments.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (2):154.
The Bounded Axiom A Forcing Axiom.Thilo Weinert - 2010 - Mathematical Logic Quarterly 56 (6):659-665.
The Strength of Mac Lane Set Theory.A. R. D. Mathias - 2001 - Annals of Pure and Applied Logic 110 (1-3):107-234.
The Ground Axiom.Jonas Reitz - 2007 - Journal of Symbolic Logic 72 (4):1299 - 1317.
The Strength of Extensionality I—Weak Weak Set Theories with Infinity.Kentaro Sato - 2009 - Annals of Pure and Applied Logic 157 (2-3):234-268.
The Bounded Proper Forcing Axiom.Martin Goldstern & Saharon Shelah - 1995 - Journal of Symbolic Logic 60 (1):58-73.
Forcing Under Anti‐Foundation Axiom: An Expression of the Stalks.Sato Kentaro - 2006 - Mathematical Logic Quarterly 52 (3):295-314.

Analytics

Added to PP index
2021-05-16

Total views
4 ( #1,286,610 of 2,533,568 )

Recent downloads (6 months)
2 ( #261,212 of 2,533,568 )

How can I increase my downloads?

Downloads

My notes