It is proved that if an uncountable cardinal κ has ineffable subset of weakly compact cardinals, then a cardinal, and Ramsey (Rowbottom, Jónsson, or subtle) J\'onsson, cardinal.

Orientation perception is not comparable across all orientations-a phenomenon commonly referred to as the oblique effect. Here, we first assessed the interaction between stimulus contrast and the oblique effect. Specifically, we examined whether the impairment in behavioral performance for oblique versus cardinal orientations is best explained by a contrast or a response gain modulation of the ...

We analyze the notion of guessing model, a way to assign combinatorial properties to arbitrary regular cardinals. Guessing models can be used, in combination with inaccessibility, to characterize various large cardinals axioms, ranging from supercompactness to rank-to-rank embeddings. The majority of these large cardinals properties can be defined in terms of suitable elementary embeddings j : ...

A set mapping on a set 5 is a function f from S into the set of subsets of 5 such that u+f(ti) (YES); AcS is called a free set (for the setmapping)if yqf(u> forall x,yeA, i.e. Anf(A)=c#, Itwasanold conjecture of Ruziewicz cl] that, if IS] = rn’ H, , and if IfcY)I< h (reS), where n is a fixed cardinal less than m, then there is a free set of cardinal m. D. LazLr [2] proved this in the case when ...

The abbreviation “PCF” stands for “Possible Cofinalities”. PCF theory was invented by Saharon Shelah to prove upper bounds on exponents of singular cardinals. The starting point of PCF theory is in the realization that the usual exponent function is too coarse for measuring the power set of singular cardinals. Consider the cardinal אω, which is the smallest singular cardinal and has countable c...