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Results tagged with set-theory
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user 167587
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.
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Must the number of smooth structures be countable or continuum?
Let $M$ be a manifold. Must the number of non-diffeomorphic smooth structures on $M$ be either countable or continuum? Could it be something in between when the continuum hypothesis fails?
Edit:
By m …
- 623
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Some "axiom of choice" and "dependent choice" issues
The answer to (2) actually depends on the exact meaning of "strictly larger", since cardinalities without choice are a mess. Working in ZF+DC, if $\mathcal{B}$ is a countably generated $\sigma$-algebr …
- 623