相关论文: A comment on "p<t"
We define a weak iterability notion that is sufficient for a number of arguments concerning $\Sigma_1$-definability at uncountable regular cardinals. In particular we give its exact consistency strength firstly in terms of the second…
We show that a point is solution of the Minty variational inequality of subdifferential type for a given function if and only if the function is increasing along rays starting from that point. This provides a characterization of the…
Let $A\subseteq \mathbb{Z}_p^2$ be a set of size $2p+1$ for prime $p\geq 5$. In this paper, we prove that $A\hat{+}A=\{a_1+a_2\mid a_1,a_2\in A, a_1\neq a_2\}$ has cardinality at least $4p$. This result is the first advancement in over two…
The Kalikow problem for a pair (lambda, kappa) of cardinal numbers, lambda > kappa (in particular kappa =2) is whether we can map the family of omega --sequences from lambda to the family of omega --sequences from kappa in a very continuous…
We give some general criteria, when kappa-complete forcing preserves largeness properties -- like kappa-presaturation of normal ideals on lambda (even when they concentrate on small cofinalities). Then we quite accurately obtain the…
We study several cardinal, and ordinal--valued functions that are relatives of Hanf numbers. Let kappa be an infinite cardinal, and let T subseteq L_{kappa^+, omega} be a theory of cardinality <= kappa, and let gamma be an ordinal >=…
We study linear $\alpha_p$-actions on affine spaces and the associated quotient singularities, using explicit stacky resolutions. We describe when the quotient singularities are log canonical, canonical or terminal, and we compute their…
Suppose that kappa is a singular cardinal of cofinality omega and GCH holds. Assume that for every n<omega the set of alphas with o(alpha)>= alpha^{+n} is unbounded in kappa.Then there is a cardinal preserving extension satisfying…
We show that in the aleph_2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of…
We prove that if ZF is consistent then ZFC+GCH is consistent with the following statement: There is for every k<omega a model of cardinality aleph_1 which is L_{infty,omega_1}-equivalent to exactly k non-isomorphic models of cardinality…
For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$ it is consistent that $2^{\kappa}$ is as large as you wish, and every function $f:\eta \to [\kappa,2^{\kappa}]\cap Card$ with $f(\alpha)=\kappa$ for $cf(\alpha)<\kappa$ is the…
In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In…
We introduce a two-parameter modification of the cofinality invariant of ideals. This allows us to include the interaction of a pair of ideals in the study of base-like structures. We find the values (cardinal numbers or well-known cardinal…
By forcing with $\mathbb{P}_{\rm max}$ over strong models of determinacy, we obtain models where different square principles at $\omega_2$ and $\omega_3$ fail. In particular, we obtain a model of $2^{\aleph_0}=2^{\aleph_1}=\aleph_2 +…
Let $\mu_p(A,B,t)=(tA^p+(1-t)B^p)^{1/p}$ denote the weighted power mean between positive operators $A$ and $B$. We show that the function $t\to \|A-\mu_p(A,B,t)\|_2$ is monotonically decreasing whenever $1/2 \leq p \leq 1$. Hence showing…
Denote by $\continuum=2^{\aleph_0}$ the cardinal of continuum. We construct an intriguing family $(P_\alpha: \alpha\in\continuum)$ of prime $z$-ideals in $\C_0(\reals)$ with the following properties: If $f\in P_{i_0}$ for some…
This paper studies cardinal invariants b_kappa and t_kappa, the natural generalizations of the invariants b and t to a regular cardinal kappa.
Assuming the P-ideal dichotomy, we attempt to isolate those cardinal characteristics of the continuum that are correlated with two well-known consequences of the proper forcing axiom. We find a cardinal invariant $\mathfrak{x}$ such that…
Carter, Jelsovsky, Kamada, Langford and Saito have defined an invariant of classical links associated to each element of the second cohomology of a finite quandle. We study these invariants for Alexander quandles of the form Z[t,t^{-1}]/(p,…
We show relative to strong hypotheses that patterns of compact cardinals in the universe, where a compact cardinal is one which is either strongly compact or supercompact, can be virtually arbitrary. Specifically, we prove if V is a model…