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Generalizing primitive recursive arithmetic

Algebra & Discrete Mathematics

Speaker: Andre Kornell, UC Davis
Location: 2112 MSB
Start time: Thu, May 11 2017, 4:10PM

[Please note the special date!]

Skolem defined a formal theory PRA of primitive recursive functions as a formalization of finitist arithmetic. I will exhibit a presentation of PRA that allows limited quantification, with the property that every sentence in a deduction may be verified computationally. I will also exhibit an extension of PRA that additionally proves that if any sentence in one of its own deductions is true, then so is the next sentence. Rathjen defined a variant formal theory PRS of primitive recursive set functions. I will exhibit an extension of PRS that satisfies the same properties as the extension of PRA just mentioned, and that is strong enough to formalize ZFC, the accepted foundational theory for standard mathematical practice.