Related papers: Jensen's diamond principle and its relatives
We show that Vopenka's Principle and Vopenka cardinals are indestructible under reverse Easton forcing iterations of increasingly directed-closed partial orders, without the need for any preparatory forcing. As a consequence, we are able to…
We provides some new equivalent forms of collection principle over some very weak set theories after reviewing the existing ones.
We prove that for regular $\lambda$ above a strong limit singular $\mu$ certain guessing principles follow just from cardinal arithmetic assumptions. The main result is that for such $\lambda$ and $\mu$ there are coboundedly many regular…
We prove that a variety of generalized cardinal characteristics, including meeting numbers, the reaping number, and the dominating number, satisfy an analogue of the Galvin-Hajnal theorem, and hence also of Silver's theorem, at singular…
A new large-cardinal property is introduced which enables one to give a relative consistency proof of restricted versions of the reflection principles discussed by Tait in his essay "Constructing Cardinals from Below".
We introduce and axiomatize the notion of a reflective cardinal, use it to give semantics to higher order set theory, and explore connections between the notion of reflective cardinals and large cardinal axioms.
We give two results on guessing unbounded subsets of lambda^+. The first is a positive result and applies to the situation of lambda regular and at least equal to aleph_3, while the second is a negative consistency result which applies to…
The celebrated union-closed conjecture is concerned with the cardinalities of various subsets of the Boolean $d$-cube. The cardinality of such a set is equivalent, up to a constant, to its measure under the uniform distribution, so we can…
Assuming Jensen's principle diamond, there is a compact Hausdorff space X which is hereditarily Lindelof, hereditarily separable, and connected, such that no closed subspace of X is both perfect and totally disconnected. The Proper Forcing…
This letter studies the Friedkin-Johnsen (FJ) model with diminishing competition, or stubbornness. The original FJ model assumes that each agent assigns a constant competition weight to its initial opinion. In contrast, we investigate the…
We answer an open question in the theory of transducer degrees initially posed in [1] on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which…
There is much recent interest in excluded subposets. Given a fixed poset $P$, how many subsets of $[n]$ can found without a copy of $P$ realized by the subset relation? The hardest and most intensely investigated problem of this kind is…
In this paper, we study the notion of a generically extendible cardinal, which is a generic version of an extendible cardinal. We prove that the generic extendibility of $\omega_1$ or $\omega_2$ has small consistency strength, but that of a…
We argue that the correlation between the modular Hamiltonians of two causal diamonds related by a finite time translation is equal to the uncertainty in the modular Hamiltonian of the diamond in their overlap. In a separate section we…
It is proved that the consistency strength of having definable tree property for successors of all regular cardinals is the consistency strength of having proper class many small large cardinals which are defined very similar to…
In this paper, we obtain the consistency, relative to large cardinals, of the existence of dense ideals on every successor of a regular cardinal simultaneously. Using a consequent transfer principle, we show that in this model there is a…
We argue against Foreman's proposal to settle the continuum hypothesis and other classical independent questions via the adoption of generic large cardinal axioms.
Strong reflection principles with the reflection cardinal $\leq\aleph_1$ or $<2^{\aleph_0}$ imply that the size of the continuum is either $\aleph_1$ or $\aleph_2$ or very large. Thus, the stipulation, that a strong reflection principle…
The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Gr\"{u}ss Inequality. It has been reported in the literature that fragmentation (or…
In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.