We prove that in Solovay model every OD equivalence E on reals either admits an OD reduction to the equality on the set of all countable (of length < ω1 ) binary sequences, or continuously embeds E0, the Vitali equivalence. If E is a Σ1 1 (resp. Σ 1 2 ) relation then the reduction in the “either” part can be chosen in the class of all ∆1 (resp. ∆2 ) functions. The proofs are based on a topology...

This paper studies the phase transition in random Horn satissability: under the random model (n; m) in which a formula is obtained by choosing m clauses independently, uniformly at random, and with repetition from all Horn clauses in n variables, (n) = 2 n is the satissability threshold for the Horn satissability. The threshold is coarse since, if (n) = c 2 n then lim n!1 Pr 2(n;;(n)) is satiss...

We have tested a relative spectral lag (RSL) method suggested earlier as a luminosity/redshift (or distance) estimator, using the generalized method by Schaefer & Collazzi. We find the derivations from the luminosity/redshift-RSL (L/R-RSL) relation are comparable with the corresponding observations. Applying the luminosityRSL relation to two different GRB samples, we find that there exist no vi...

This paper argues that growth theory needs a more general notion of “regularity” than that of exponential growth. We suggest that paths along which the rate of decline of the growth rate is proportional to the growth rate itself deserve attention. This opens up for considering a richer set of parameter combinations than in standard growth models. Moreover, it avoids the usual oversimplistic dic...

I point out that the Oosterhoff dichotomy for globular cluster and field RR Lyrae (RRL) stars may place the strongest constraints so far on the number of dwarf spheroidal-like protogalactic fragments that may have contributed to the formation of the Galactic halo. The first calibration of the RRL period-luminosity relation in I, J , H, K taking evolutionary effects into account is provided. Pro...

This paper studies the phase transition in random Horn satissability: under the random model (n; m) in which a formula is obtained by choosing m clauses independently, uniformly at random, and with repetition from all Horn clauses in n variables, (n) = 2 n is the satissability threshold for the Horn satissability. The threshold is coarse since, if (n) = c 2 n then lim n!1 Pr 2(n;;(n)) is satiss...