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Computable analogs of cardinal characteristics: Prediction and rearrangement
Authors:Iván Ongay-Valverde  Paul Tveite
Affiliation:Department of Mathematics, University of Wisconsin–Madison, United States of America
Abstract:There has recently been work by multiple groups in extracting the properties associated with cardinal invariants of the continuum and translating these properties into similar analogous combinatorial properties of computational oracles. Each property yields a highness notion in the Turing degrees. In this paper we study the highness notions that result from the translation of the evasion number and its dual, the prediction number, as well as two versions of the rearrangement number. When translated appropriately, these yield four new highness notions. We will define these new notions, show some of their basic properties and place them in the computability-theoretic version of Cichoń's diagram.
Keywords:Set theory  Computability theory  Cardinal characteristics  Cichon diagram  Forcing
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