The tag has no wiki summary.

learn more… | top users | synonyms

7
votes
0answers
131 views

Does $\mathsf{fReR}_0$ prove the existence of the cartesian product of two sets

$\mathsf{fReR}_0$ is the set-theoretical system whose axioms consist of: (1) Axiom of extensionality: $\forall z\in x\ (z\in y)\wedge\forall z\in y\ (z\in x)\rightarrow x=y$ (2) Axiom of empty set: ...
3
votes
2answers
222 views

A question on Gandy-Jensen system and the rudimentary functions

Let $\mathrm{R}_0,\cdots,\mathrm{R}_8$ be the following functions: $\mathrm{R}_0(x,y)=\{x,y\}$ $\mathrm{R}_1(x,y)=x-y$ $\mathrm{R}_2(x)=\bigcup x$ $\mathrm{R}_3(x,y)=x\times y$ ...