On strong forms of reflection in set theory | Zendy

Friedman SyDavid | Zendy; Honzik Radek | Zendy

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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.

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