# An external approach to set theory

@inproceedings{Quinn2021AnEA, title={An external approach to set theory}, author={Frank Quinn}, year={2021} }

3 Logical domains, and quantification 11 3.1 Logical domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Cantor-Bernstein theorem . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.4 Subdomains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.5 Logical pairings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

## References

SHOWING 1-10 OF 16 REFERENCES

As before, 'pfn' denotes partially-defined functions. Again as in §4.2, a partially-defined function f : A → B is R-recursive if: 1. dom[f ] is λ-transitive; and 2. for every c ∈ dom

Choice' is a primitive axiom

Choice) There is a partially-defined function ch : Σ → Σ with domain a ∈ Σ | N

Extension' is equivalent to injectivity of the adjoint of , and this is a design requirement in the construction

Frank Quinn A category-friendly approach to set theory

Infinity' is a primitive axiom in the system used here

Replacement) Suppose f : Σ → Σ is an appropriate function. Then the f image of a set is a set (see note 6)

Separation) If P is an appropriate logical function on Σ (a "property

The domains [a, #] are relaxed sets because they are bounded subdomains of Q ∞ W

The maximal R-recursive function f : A → Q ∞ W has domain A, and the recursion condition implies that f is a morphism (A, λ) → (Q ∞ W, )