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Results tagged with set-theory
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user 122189
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.
9
votes
1
answer
319
views
Embeddings of linear orders in $\wp(\omega)/Fin$ under Martin's axiom
We know that, under MA, every linear order $(X,\le)$ with $|X|<\mathfrak c$ embedds in $\wp(\omega)/Fin$. Does this hold for linear orders with cardinality $\mathfrak c$?
- 419
3
votes
2
answers
321
views
Delta systems under Martin's Axiom
The $\Delta$-system Lemma states that given an uncountable family $\mathcal C$ of sets with finite intersection there exist an uncountable subfamily $\mathcal D$ of $\mathcal C$ and a finite set $\Del …
- 419
2
votes
0
answers
82
views
Separability of $(\kappa,\mathfrak c)$-gaps in $\wp(\omega)/Fin$
K. Kunen proved that it is relatively consistent with Martin´s Axiom that every $(\omega_1,\mathfrak c)$-gap and every $(\mathfrak c,\mathfrak c)$-gap can be separated in $\wp(\omega)/Fin$. What about …
- 419
3
votes
1
answer
163
views
Nonmetrizable Corson compacta with ccc
It is known that under $MA+ \neg CH$, every Corson compact space with the countable chain condition (ccc) is merizable. It is also known that, under $CH$, there exist nonmetrizable Corson compact spac …
- 419
9
votes
1
answer
384
views
Embeddings of Boolean algebras in $\wp(\omega)/Fin$
If we assume MA+¬CH, then every boolean algebra with cardinality smaller than the continuum embeds in ℘(ω)/Fin. A proof of this result can be found in Theorem 1.1, Chapter 8 of the book "Hausdorff gap …
- 419