Forcing a set model of    Z  3    + Harrington's Principle | Zendy

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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.

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