Dependence is ubiquitous in the sciences and everyday life. At the same time dependence has the interesting, even mysterious property that it manifests itself only in a multitude, not in a single event. The taste of wine depends on the vintage. Eye color may depend on a gene. Parking is easy depending on the day. Such facts are revealed only in repeated observations. In contrast to these multitude truths, there are facts such as 2+2=4 which seemingly could not be otherwise. The polarity between multitude truths and absolute certainty is the focus of this novel project. We develop a logic of dependence proposing it as a core logic, underlying distinct areas, especially foundations of quantum mechanics. We also pursue a program in set theory, involving inner models, infinitary logic, and Generalized Baire Spaces.

2025

2029