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The Cichoń diagram for degrees of relative constructibility
Author(s) -
Switzer Corey Bacal
Publication year - 2020
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201900062
Subject(s) - diagram , mathematics , axiom , analogy , construct (python library) , calculus (dental) , computer science , epistemology , geometry , programming language , statistics , medicine , dentistry , philosophy
Following a line of research initiated in [4], we describe a general framework for turning reduction concepts of relative computability into diagrams forming an analogy with the Cichoń diagram for cardinal characteristics of the continuum. We show that working from relatively modest assumptions about a notion of reduction, one can construct a robust version of such a diagram. As an application, we define and investigate the Cichoń diagram for degrees of constructibility relative to a fixed inner model W . Many analogies hold with the classical theory as well as some surprising differences. Along the way, we introduce a new axiom stating, roughly, that the constructibility diagram is as complex as possible.