Bounding by canonical functions, with CH

Bounding and dominating number of families of functions on N

We pursue the study of families of functions on the natural numbers, with emphasis here on the bounded families. The situation being more complicated than the unbounded case, we attack the problem by classifying the families according to their bounding and dominating numbers, the traditional scheme for gaps. Many open questions remain.

Bounding the decay of oscillatory integrals with a constructible amplitude function and a globally subanalytic phase function

We call a function "constructible" if it has a globally subanalytic domain and can be expressed as a sum of products of globally subanalytic functions and logarithms of positively-valued globally subanalytic functions. Our main theorem gives uniform bounds on the decay of parameterized families of oscillatory integrals with a constructible amplitude function and a globally subanalytic phase function, assuming that the amplitude function is integrable and that the phase function satisfies a certain natural condition called the hyperplane condition. As a simple application of this theorem, we al…

通过1维函数的乘积来界定2维函数

Bounding 2D Functions by Products of 1D Functions

研究在ZFC下，2维函数能否被1维函数的乘积上界所界定，并探讨在ZF+俱乐部滤子正常性条件下，可测基数的 Mitchell 层次。

Higher Dimensional Cardinal Characteristics for Sets of Functions II

We study the values of the higher dimensional cardinal characteristics for sets of functions $f:ω^ω\to ω^ω$ introduced by the second author. We prove that while the bounding numbers for these cardinals can be strictly less than the continuum, the dominating numbers cannot. We compute the bounding numbers for the higher dimensional relations in many well known models of $\neg\mathsf{CH}$ such as the Cohen, random and Sacks models and, as a byproduct show that, with possibly one exception, for the bounding numbers there are no $\mathsf{ZFC}$ relations between them beyond those in the higher dime…