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math.LO2022
An axiomatic approach to higher order set theory
Alec Rhea
Higher order set theory has been a topic of interest for some time, with recent efforts focused on the strength of second order set theories [KW16]. In this paper we strive to pres…
math.LO2022
An axiomatic approach to the multiverse of sets
Alec Rhea
Recent work in set theory indicates that there are many different notions of 'set', each captured by a different collection of axioms, as proposed by J. Hamkins in [Ham11]. In this…
math.LO2017★ 1 cited
The Ordinals as a Consummate Abstraction of Number Systems
Alec Rhea
In the course of many mathematical developments involving 'number systems' like etc., it sometimes becomes necessary t…