Generic Sets and Arbitrary Objects
Bibliographic Data
| ID | 21364139 |
|---|---|
| Authors | Giorgio Venturi (0000-0001-9089-4340, Dipartimento di Civiltà e forme del sapere Università di Pisa Pisa Italy, corresponding author) |
| Year | 2026 |
| Publication date | 2026-02-08 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Noûs (JOURNAL) |
| Journal identifiers | ISSN: 0029-4624 • E-ISSN: 1468-0068 |
| Publisher | Wiley (PUBLISHER • GB) |
| DOI | 10.1111/nous.70039 |
| OpenAlex | W7128358698 |
| Language | EN |
| References cited | 4 |
In this paper, I investigate whether generic sets, in the context of the theory of forcing, can be understood as arbitrary objects in the sense of Fine or Horsten. I will provide a partially positive and partially negative answer. Specifically, the answer will depend on whether I will consider generic sets as objects or as names. I also compare our perspective with Horsten's view on Boolean‐valued sets as arbitrary objects. I conclude by suggesting that there is a cluster of notions semantically similar to arbitrariness that gives rise to useful objects in mathematics
Algebra over a field · Arbitrariness · Context (archaeology) · Object (grammar) · Perspective (graphical) · Set (abstract data type) · Set theory · Advanced Topology and Set Theory · Computability, Logic, AI Algorithms · Philosophy and Theoretical Science
| Citation velocity | historical |
|---|---|
| Highly cited | No |