Bulletin of Symbolic Logic: Volume 15 - Issue 4

Mass Problems and Measure-Theoretic Regularity
Stephen G. Simpson
Published online by Cambridge University Press:

15 January 2014, pp. 385-409
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A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an Fσ set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measuretheoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility. We build some ω-models of RCA0 which are relevant for the reverse mathematics of measure-theoretic regularity.

Games for Truth
P. D. Welch
Published online by Cambridge University Press:

15 January 2014, pp. 410-427
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We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of .

Bulletin of Symbolic Logic