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Results tagged with lo.logic
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user 3489
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
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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
0
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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
2
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3
answers
2k
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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