Original Paper

Destructibility of stationary subsets of Pκλ

  1. Sakaé Fuchino,
  2. Greg Piper

Article first published online: 28 SEP 2005

DOI: 10.1002/malq.200510009

Issue

Mathematical Logic Quarterly

Mathematical Logic Quarterly

Volume 51, Issue 6, pages 560–569, November 2005

Additional Information

How to Cite

Fuchino, S. and Piper, G. (2005), Destructibility of stationary subsets of Pκλ. Mathematical Logic Quarterly, 51: 560–569. doi: 10.1002/malq.200510009

Author Information

  1. Graduate School of Science and Technology Kobe University, Nada Kobe 657-8501, Japan

Publication History

  1. Issue published online: 28 SEP 2005
  2. Article first published online: 28 SEP 2005
  3. Manuscript Accepted: 6 JUL 2005
  4. Manuscript Received: 18 JUN 2005

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Keywords:

  • Stationary sets;
  • internally approachable models;
  • club shooting;
  • Pκλ

Abstract

For a regular cardinal κ with κ<κ = κ and κ ≤ λ , we construct generically (forcing by a < κ-closed κ+-c. c. p. o.-set ℙ0) a subset S of {x ∈ Pκλ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense (FIAκλ -stationary in our terminology) but the stationarity of S can be destroyed by a κ+-c. c. forcing ℙ* (in Vℙ) which does not add any new element of Pκλ . Actually ℙ* can be chosen so that ℙ* is κ-strategically closed. However we show that such ℙ* itself cannot be κ-strategically closed or even <κ-strategically closed if κ is inaccessible. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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