S-forcing IIa: Adding diamonds and more applications: Coding sets, Arhangel'skii's problem and ℒ {Mathematical expression}

Saharon Shelah, Lee J. Stanley, John P. Burgess

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We continue our earlier paper [20] by proving the equivalence, for regular κ>ω, of the existence of (κ, 1) morasses with built-in {black diamond suit} sequences and a strengthening, SK{lozenge, open}, of the forcing principle, SK{lozenge, open} of [20]. We obtain various applications of SK{lozenge, open}, to wit: the existence of a stationary subset of [K+]<K with sup as coding function, the existence of a counterexample to Arhangel'skii's conjecture (κ=א1) and compactness, axiomatizability and transfer properties for the Magidor-Malitz language ℒ {Mathematical expression} (κ=א1).

Original languageEnglish (US)
Pages (from-to)1-65
Number of pages65
JournalIsrael Journal of Mathematics
Volume56
Issue number1
DOIs
StatePublished - Feb 1986

All Science Journal Classification (ASJC) codes

  • General Mathematics

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