A dilemma in the philosophy of set theory
type: Item
instance of: scholarly article
title: A dilemma in the philosophy of set theory
zbMATH Open document ID: 0832.03026
published in: Notre Dame Journal of Formal Logic
publication date: 1996-03-05T00:00:00Z
review text: The author considers a weak form \(\text{BL}_1\) of Bernays' set theory, e.g. determined as NBG with \(\Pi^1_1\)-reflection. Then he shows that \(\text{BL}_1\) proves \(\Delta^1_1 (\text{NBG})\)- comprehension, but that on the other hand \(\Delta^1_1 (\text{NBG})\)-comprehension fails in the case that one assumes that only classes exist which are definable by set-theoretical predicates with set parameters. As \(\text{BL}_1\) is a kind of minimal framework for large cardinals, this means that ``non-predicative'' classes are indispensable for large cardinals.
reviewed by: Siegfried J. Gottwald
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03E10
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 769237
zbMATH Keywords: reflection principles
zbMATH Keywords: philosophy of set theory
zbMATH Keywords: large cardinals
author: Ralf Schindler
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1040511351
OpenAlex ID: W2065861009
cites work: Q5557895
cites work: Q4108330
cites work: Proper classes
cites work: Believing the axioms. I
cites work: Some impredicative definitions in the axiomatic set theory
cites work: Q4088821
cites work: On a set theory of bernays
DOI: 10.1305/NDJFL/1040511351
description: scientific article; zbMATH DE number 769237