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Results tagged with set-theory
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user 76572
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.
20
votes
3
answers
2k
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Ordering of large cardinals by cardinality
Let Type A and Type B be two types of large cardinals from, say, Cantor's Attic (http://cantorsattic.info/Upper_attic)
Now assuming that ZFC + Type A + Type B is consistent (ie, both Type A and Type …
- 801
2
votes
1
answer
1k
views
Wholeness Axiom and Ultimate L
From what I understand:
The Wholeness Axiom(s) is/are the "ultimate axioms of infinity", bordering on inconsistency with ZFC.
Ultimate L (Completion of ZFC) attempts to extend the orderly world of c …
- 801
13
votes
4
answers
1k
views
Large cardinal consistency strength and size
My understanding is that large cardinals are ordered by "consistency strength", but how does this correlate with their size (cardinality)?
More specifically, are there any systematic results on the l …
- 801
31
votes
5
answers
3k
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Why should we care about "higher infinities" outside of set theory?
Let's say you are a prospective mathematician with some addled ideas about cardinality.
If you assumed that the natural numbers were finite, you'd quickly vanish in a puff of logic. :)
If you though …
- 801
6
votes
1
answer
1k
views
Replacing Axiom of Choice with Axiom of Countable Choice
Many people find ACC more intuitive than AC ("Pick something from the first set, then something from the second set, then...) and it also doesn't lead to "controversial consequences" (See for eg: Pecu …
- 801