Journal of Symbolic Logic

Semistationary and stationary reflection

Hiroshi Sakai

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Abstract

We study the relationship between the semistationary reflection principle and stationary reflection principles. We show that for all regular cardinals λ ≥ ω2 the semistationary reflection principle in the space [λ]ω implies that every stationary subset of Eλω := { α ∈ λ | cf(α) = ω } reflects. We also show that for all cardinals λ ≥ ω3 the semistationary reflection principle in [λ]ω does not imply the stationary reflection principle in [λ]ω.

Article information

Source
J. Symbolic Logic, Volume 73, Issue 1 (2008), 181-192.

Dates
First available in Project Euclid: 16 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1208358748

Digital Object Identifier
doi:10.2178/jsl/1208358748

Mathematical Reviews number (MathSciNet)
MR2387938

Zentralblatt MATH identifier
1149.03039

Subjects
Primary: 03E55: Large cardinals
Secondary: 03E35: Consistency and independence results

Keywords
Semistationary reflection Stationary reflection

Citation

Sakai, Hiroshi. Semistationary and stationary reflection. J. Symbolic Logic 73 (2008), no. 1, 181--192. doi:10.2178/jsl/1208358748. https://projecteuclid.org/euclid.jsl/1208358748


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