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Results tagged with set-theory
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user 3489
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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definition of the set of natural numbers
After some reasoning I put down this one. If you know that $A$ is inductive and that $N_B=\{x\in B:\forall(I)(x\in I)\}$ where $I$ varies over inductive sets, then it follows that $N_B=\{x\in B:x\in A …
- 31
0
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definition of the set of natural numbers
If I understood correctly, one could associate to every set $A$ (no matter if $A$ is inductive or not) the set $N_A=\{x\in A:\forall(I)(x\in I)\}$ where $I$ varies over inductive sets. Then one could …
- 31
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3
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definition of the set of natural numbers
How can the set $N$ of natural numbers be defined from the point of view of the ZF axiomatic set theory provided the concept of inductive set? Hrbacek-Jech (page 41) says that $N=\{x\in A:\forall(I)(x …
- 31