2019/02/20 by Andrew Powell, Powell, Andrew
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Theory of Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO
paper · pdf · doi:10.48550/arxiv.1902.07373
7 pages, no figures. Experimental paper; comments welcome; minor changes made to justify (++) principle
openalex publication_date 2019/02/20 · arxiv created 2020/01/12 · arxiv updated 2020/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular order for example). The construction approach is then applied to searching for a mathematical object in a set, and a logarithm-time search algorithm outlined which applies to a set X of all binary sequences of length ordinal β with a binary label appended to each sequence to indicate that sequence is a member of X or not. It follows that deciding membership of a set for a given binary sequence of length of binary sequence of cardinal length β takes β+1 bits, which is shown to be equivalent to the Generalised Continuum Hypothesis on the assumption that information is minimised when a mathematical object is created.