## Gödel's program for new axioms: Why, where, how and what? (1996)

Venue: | IN GODEL '96 |

Citations: | 16 - 6 self |

### BibTeX

@INPROCEEDINGS{Feferman96gödel'sprogram,

author = {Solomon Feferman},

title = {Gödel's program for new axioms: Why, where, how and what?},

booktitle = {IN GODEL '96},

year = {1996},

pages = {3--22},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

From 1931 until late in his life (at least 1970) Gödel called for the pursuit of new axioms for mathematics to settle both undecided number-theoretical propositions (of the form obtained in his incompleteness results) and undecided set-theoretical propositions (in particular CH). As to the nature of these, Gödel made a variety of suggestions, but most frequently he emphasized the route of introducing ever higher axioms of in nity. In particular, he speculated (in his 1946 Princeton remarks) that there might be a uniform (though non-decidable) rationale for the choice of the latter. Despite the intense exploration of the "higher infinite" in the last 30-odd years, no single rationale of that character has emerged. Moreover, CH still remains undecided by such axioms, though they have been demonstrated to have many other interesting set-theoretical consequences. In this paper, I present a new very general notion of the "unfolding" closure of schematically axiomatized formal systems S which provides a uniform systematic means of expanding in an essential way both the language and axioms (and hence theorems) of such systems S. Reporting joint work with T. Strahm, a characterization is given in more familiar terms in the case that S is a basic