Abstract
The results established in this paper are in connection with the Relative Internal Set Theory (R.I.S.T.). The main result is the general principle of choice: Let α be a level and let Φ(x, y) be anαexternalαbounded formula of the language of R.I.S.T.. Suppose that to each elementx, dominated by α, corresponds an elementy x such that Φ(x, y x ) holds, then there exists a function of choice ψ such that, which is a very general principle of choice, for everyx dominated by α, Φ(x, ψ(x)) holds. More than that, we establish that if all the elementsy x are uniformly dominated by a level β then we can prescribe that the function of choice is also dominated by β.
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Péraire, Y. Some extensions of the principles of idealization transfer and choice in the relative internal set theory. Arch Math Logic 34, 269–277 (1995). https://doi.org/10.1007/BF01469384
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DOI: https://doi.org/10.1007/BF01469384