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Results tagged with set-theory
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user 4085
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.
4
votes
Does the axiom of specification prevent writing any proof?
Your definition of the rule of universal introduction is wrong. The usual rule for universal introduction says that if $\Sigma\vdash\phi$ and $x$ is a variable that does not occur free in $\Sigma$ th …
- 1,439
5
votes
1
answer
364
views
Conservation of Hyperarithmetic Sentences over AC and CH.
I know that arithmetic sentences are conserved under the addition of the axiom of choice and the continuum hypothesis to ZF (i.e. ($ZF+AC \vdash \phi$ iff $ZF \vdash \phi$) and ($ZF+CH \vdash \phi$ if …
- 1,439
4
votes
Set theories that do require the existence of urelements?
Nominal logic is based on the Frænkel-Mostowski permutation model of set theory. In particular Nominal logic has a freshness axiom that states ${\forall}x. {\exists}a \in \mathbb{A}. a \# x$, where $ …
- 1,439