2013/04/16 by Beklemishev, Lev
#03F45 03B45 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1304.4396
We deal with the fragment of modal logic consisting of implications of formulas built up from the variables and the constant `true' by conjunction and diamonds only. The weaker language allows one to interpret the diamonds as the uniform reflection schemata in arithmetic, possibly of unrestricted logical complexity. We formulate an arithmetically complete calculus with modalities labeled by natural numbers and ω, where ωcorresponds to the full uniform reflection schema, whereas n