Related papers: Stranger Things about Forcing without AC
We show explicitly, for different types of extremal black holes, that test fields satisfying the null energy condition at the event horizon cannot violate the weak cosmic censorship conjecture. This is done by checking, in each case, that…
Let I be a sigma-ideal sigma-generated by a projective collection of closed sets. The forcing with I-positive Borel sets is proper and adds a single real r of an almost minimal degree: if s is a real in V[r] then s is Cohen generic over V…
Orderability, weak orderability and the existence of continuous weak selections on filter spaces (i.e., spaces with a single non-isolated point) and their products are discussed. We prove that a closed continuous image X of a suborderable…
We introduce a new method for building models of CH, together with $\Pi_2$ statements over $H(\omega_2)$, by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only $\aleph_1$-many of…
We propose an AC-independent proof of the existence of a non-measurable set as a consequence of the Hahn-Banach theorem of functional analysis which is known to be strictly weaker than AC.
A transitive model $M$ of ZFC is called a ground if the universe $V$ is a set forcing extension of $M$. We show that the grounds of $V$ are downward set-directed. Consequently, we establish some fundamental theorems on the forcing method…
Because of the mass density-dependence, an extra term should be added to the expression of pressure. However, it should not appear in that of energy according to both the general ensemble theory and basic thermodynamic principle. We give a…
We investigate the weak cosmic censorship conjecture in Kerr-(anti-)de Sitter black holes under the scattering of a scalar field. We test the conjecture in terms of whether the black hole can exceed the extremal condition with respect to…
The exact conditions on valid pointer states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any pointer state with vanishing probability current density. This condition is found both for…
A description of strange quark matter at finite temperature is given, with emphasis on the inclusion of finite size effects. For massless quarks all thermodynamic quantities can be evaluated analytically, while the case of massive quarks…
We introduce the forcing property "almost strong properness" which sits between properness and strong properness. As an application, we introduce a simple forcing with finite conditions to force $\rm MRP$.
We prove some iteration theorems for a certain class of $\kappa^+$-cc forcing posets.
Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I…
Passive filters allowing the exchange of particles in a narrow band of energy are currently used in micro-refrigerators and energy transducers. In this letter, we analyze their thermal properties using linear irreversible thermodynamics and…
We demonstrate that theories $\text{Z}^-$, $\text{ZF}^-$, $\text{ZFC}^-$ (minus means the absence of the Power Set axiom) and $\text{PA}_2$, $\text{PA}_2^-$ (minus means the absence of the Countable Choice schema) are equiconsistent to each…
Conventionally, the strong-$CP$ problem is assumed to be a naturalness puzzle, with the axion solution sometimes viewed as an ad hoc fix. Gravity is either ignored or taken as a threat for the global Peccei-Quinn symmetry. We explain that…
The purpose of this work is threefold: (i) extend shadowing theory for discontinuous and non-invertible systems, (ii) consider more general classes of perturbations (for example, small only on average), (iii) establish a general theory…
We examine the possibility that thermal, rather than quantum, fluctuations are responsible for seeding the structure of our universe. We find that while the thermalization condition leads to nearly Gaussian statistics, a Harrisson-Zeldovich…
The Casimir effect between metal surfaces has now been well-verified at the few-percent level experimentally. However, the temperature dependence has never been observed in the laboratory, since all experiments are conducted at room…
We prove (ZF+DC) e.g. : if mu =|H(mu)| then mu^+ is regular non measurable. This is in contrast with the results for mu = aleph_{omega} on measurability see Apter Magidor [ApMg]