Definition:Standard Structure
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Definition
The structure $\struct {A, \RR}$ is called a standard structure if and only if:
- $\RR = \Epsilon \cap \paren { A \times A }$ where $\Epsilon$ denotes the epsilon relation and $\times$ denotes the Cartesian product.
With a standard structure, $\struct {A, \RR} \models p$ shall be abbreviated:
- $A \models p \iff \struct {A , E \cap \paren {A \times A} } \models p$
Sources
- 1971: Gaisi Takeuti: Introduction to Axiomatic Set Theory: $\S 12.2$, $\S 12.3$