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Results tagged with set-theory
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user 165275
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
11
votes
What can be preserved in mathematics if all constructions are carried out in ZF?
One of the standard texts which presents functional analysis only based on ZF+DC is the monograph (consisting of 3 volumes) Henry G. Garnir, Marc de Wilde, and Jean Schmets, Analyse Fonctionnelle.
Als …
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5
votes
BCT equivalent to DC
Yet another formulation of Blair's proof is in M. Väth, Topological Analysis, DeGruyter 2012.
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2
votes
Standard models of N and R: An Alice/Bob approach
This is way too long for a remark, therefore I post it as an answer.
Although I agree with the previous answers that there is probably no clear “intended” model of set theory, there are perhaps two pr …
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1
vote
Axiom of Countable Choice and meager sets
What is your definition of meager in (ZF)? Being a countable union of nowhere dense sets? In that case, the given argument about the failure of (UMM) in (ZF) is not clear: It is not obvious (to me) th …
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1
vote
The Tarski-Lindenbaum theorem of the middle value
Not a very satisfactory answer, but some considerations to the proof of the MV theorem:
One might think that analogously to the proof of CBS (see e.g. Joel David Hamkins answer how to use KT for that …
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