# Questions tagged [transfinite-induction]

Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers.

140 questions
Filter by
Sorted by
Tagged with
41 views

• 1,104
1 vote
81 views

• 2,391
1 vote
68 views

### How to show that the Zermelo hierarchy is really a hierarchy?

In Cameron's Sets, Logic and Categories (p. 48-49), he sets out prove the following fact about the Zermelo hierarchy $V$, namely, that $V_\alpha\subseteq V_{s(\alpha)}$ for all ordinals $\alpha$. His ...
• 1,719
104 views

### Construct an additive group by transfinite induction

I know one way to construct a Bernstein set that is an additive group.Here is the way that I know. $\{P_\xi\colon \xi<\mathfrak c\}$ all nonempty perfect subsets of $\Bbb R.$ Choose, by recursion ...
• 2,391
1 vote
106 views

### Complement of the product of Bernstein set and meager set

Assume $M\subset\mathbb R$ be a meager set with cardinality $\mathfrak c.$ I want to construct a Bernstein set $B$ such that $\mathbb R\setminus(B\cdot M)$ has cardinality $\mathfrak c$ , \$B\cdot M=\{...
• 2,391
1 vote