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Forcing a set model of Z 3 + Harrington's Principle
Author(s) -
Cheng Yong
Publication year - 2015
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.201300072
Subject(s) - forcing (mathematics) , mathematics , statement (logic) , cardinal number (linguistics) , regular cardinal , set (abstract data type) , order (exchange) , discrete mathematics , calculus (dental) , mathematical economics , epistemology , mathematical analysis , computer science , philosophy , linguistics , medicine , dentistry , finance , economics , programming language
Let Z 3 denote third order arithmetic. Let Harrington's Principle, HP , denote the statement that there is a real x such that every x ‐admissible ordinal is a cardinal in L . In this paper, assuming there exists a remarkable cardinal with a weakly inaccessible cardinal above it, we force a set model ofZ 3 + HP via set forcing without reshaping.