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Results tagged with set-theory
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user 4534
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.
2
votes
What are the known implications of "There exists a Reinhardt cardinal" in the theory "ZF + j"?
This answer is confined to Question 3. I suggest that the Axiom of Choice (AC) be regarded as placing a sharp bound on reflection. In particular, for an elementary embedding j with critical point κ an …
- 81
3
votes
Some questions about Ackermann set theory
The answer to your question is "Yes."
In trying to understand why Ackermann nonetheless wanted to distinguish proper classes such as V from sets - where V is the proper class of all sets, taken here …
- 81
1
vote
Properties of collections (functions) that make them proper classes (uncomputable)
One plausible necessary condition for a collection c to satisfy the meta-property in question is tthe following: the existence of c must not be a logical consequence of either ZFC or any large cardina …
- 81