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Reflection of Long Game Formulas
Author(s) -
Heikkilä Heikki,
Väänänen Jouko
Publication year - 1994
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.19940400307
Subject(s) - uncountable set , mathematics , reflection (computer programming) , mathematics subject classification , compact space , theme (computing) , reflection principle (wiener process) , subject (documents) , set (abstract data type) , calculus (dental) , mathematical economics , discrete mathematics , pure mathematics , computer science , medicine , knowledge management , innovation diffusion , countable set , diffusion process , dentistry , geometric brownian motion , library science , programming language , operating system
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‐II 1 1 reflection (or ∑ 1 ‐compactness). We show that admissible sets such as H (ω 2 ) and L ω2 which fail to have strict‐II 1 1 reflection, may or may not, depending on set‐theoretic hypotheses satisfy one or both of these weaker forms. Mathematics Subject Classification : 03C70, 03C75.