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Results tagged with set-theory
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user 468
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.
38
votes
Accepted
Do there exist non-PIDs in which every countably generated ideal is principal?
No such ring exists.
Suppose otherwise. Let $I$ be a non-principal ideal, generated by a collection of elements $f_\alpha$ indexed by the set of ordinals $\alpha<\gamma$ for some $\gamma$. Consid …
- 6,327
3
votes
2
answers
648
views
Can this informal argument (for the fact that almost all reals in the unit interval are irra...
In the textbook from which I am teaching a Discrete Math course, the authors propose randomly generating an infinite sequence of decimal digits $d_1, d_2, \dots$. We are to think of this as the decim …
- 6,327
7
votes
Infinite Partitions of the Primes and Sums of Reciprocals (Revised)
The following is rather more simple-minded that what you are suggesting.
Let's say we have a deck of cards, with the cards labelled by the primes in order. We are going to think of constructing th …
- 6,327