Arithmetic with Fusions

Jeffrey Ketland, Thomas Schindler


In this article, the relationship between second-order comprehen- sion and unrestricted mereological fusion (over atoms) is clarified. An extension PAF of Peano arithmetic with a new binary mereological notion of “fusion”, and a scheme of unrestricted fusion, is introduced. It is shown that PAF interprets full second-order arithmetic, Z2.


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