Mathematical Logic Quarterly

Reflection of Long Game Formulas

Journal Article


We study game formulas the truth of which is determined by a semantical game of uncountable length. The main theme is the study of principles stating reflection of these formulas in various admissible sets. This investigation leads to two weak forms of strict‐II11 reflection (or ∑1‐compactness). We show that admissible sets such as H2) and Lω2 which fail to have strict‐II11 reflection, may or may not, depending on set‐theoretic hypotheses satisfy one or both of these weaker forms.

Mathematics Subject Classification: 03C70, 03C75.

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