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math.LO2026
Idealizing Useful Fictions in Omega Grounded Arithmetic
Bryan Ford
Grounded arithmetic is a family of formal systems for reasoning about computation in which a statement may be asserted only when a terminating computation backs it; the logics are…
math.LO2026
Internal Reasoning and Consistency in Reflective Grounded Arithmetic
Bryan Ford
Reflective Grounded Arithmetic (RGA) is a paracomplete arithmetic allowing direct expression of any general-recursive computation. Every RGA term is a program and truth is grounded…
math.LO2026
Computable Quantification in Reflective Grounded Arithmetic
Bryan Ford
Informal statements of Gödel's incompleteness theorems often run: "any consistent formal system with arithmetic has true but unprovable statements." That reading assumes a classica…