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On strong forms of reflection in set theory
Author(s) -
Friedman SyDavid,
Honzik Radek
Publication year - 2016
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.201400047
Subject(s) - reflection (computer programming) , generalization , reflection principle (wiener process) , statement (logic) , mathematics , set (abstract data type) , calculus (dental) , natural (archaeology) , pure mathematics , epistemology , mathematical analysis , computer science , philosophy , history , medicine , knowledge management , innovation diffusion , dentistry , diffusion process , archaeology , geometric brownian motion , programming language
In this paper we review the most common forms of reflection and introduce a new form which we call sharp‐generated reflection . We argue that sharp‐generated reflection is the strongest form of reflection which can be regarded as a natural generalization of the Lévy reflection theorem. As an application we formulate the principle sharp‐maximality with the corresponding hypothesis IMH # . The statement IMH # is an analogue of the IMH (Inner Model Hypothesis, introduced in [3][S.‐D. Friedman, 2006]) which is compatible with the existence of large cardinals.