Related papers: Stranger Things about Forcing without AC
Many forcing notions obtained using the creature technology are naturally connected with certain integer games.
The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that any model of a sufficiently rich fragment of those theories…
Forcing axioms are generalizations of Baire category principles that allow one to intersect more dense open sets and to do so in a wider variety of circumstances. In this paper we introduce two new forcing axioms related to posets which…
We answer a question of Moore by building a forcing extension satisfying measuring together with CH. The construction works over any model of ZFC and can be described as a forcing iteration with countable structures as side conditions and…
As a charged spinning fermion drops into a charged rotating BTZ black hole, we investigate the laws of thermodynamics and weak cosmic censorship conjecture with and without pressure respectively. For the case without pressure, the first…
We introduce a forcing that adds a $\square(\aleph_2,\aleph_0)$-sequence with countable conditions under CH. Assuming the consistency of a weakly compact cardinal, we can find a forcing extension by our new poset in which both…
We define a nontrivial version of the square principle $\Box_\omega$, which we then show consistent by means of forcing with finite conditions. This paper has been withdrawn by the author due to the fact that the presented $\Box_\omega$ can…
The foundations of forcing theory are reworked to streamline the presentation and to show how the most basic results are applicable in very general contexts.
These are lecture notes from a course I gave at the University of Wisconsin during the Spring semester of 1993. Part 1 is concerned with Borel hierarchies. Section 13 contains an unpublished theorem of Fremlin concerning Borel hierarchies…
The effect of magnetic field on the structure properties of hot spin polarized strange quark stars has been investigated. For this purpose, we use the MIT bag model with a density dependent bag constant to calculate the thermodynamic…
An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing such a tree,…
Justin Moore's weak club-guessing principle $\mho$ admits various possible generalizations to the second uncountable cardinal. One of them was shown to hold in ZFC by Shelah. A stronger one was shown to follow from several consequences of…
We present a systematic study of the method of "norms on possibilities" of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the…
We show that splitting forcing does not have the weak Sacks property below any condition, answering a question of Laguzzi, Mildenberger and Stuber-Rousselle. We also show how some partition results for splitting trees hold or fail and we…
Assuming that the universe is a system obedient to known thermodynamic laws and equations, here we explore whether it is a possibility for the universe to exist and evolve without any cosmic structure or force necessarily emerging within…
The realization of a Mott insulating state in a system of ultracold fermions comprising far more internal components than the electron, provides an avenue for probing many-body physics that is difficult to access in solids.
We develop a toolbox for forcing over arbitrary models of set theory without the axiom of choice. In particular, we introduce a variant of the countable chain condition and prove an iteration theorem that applies to many classical forcings…
Boban Velickovic asked the following question: Is there a nontrivial forcing notion with the Sacks property which is also ccc? A ``definable'' variant of this question has been answered in [Sh:480] (math.LO/9303208): Every nontrivial…
We critically revisit the issue of power-law running in models with extra dimensions. The general conclusion is that, in the absence of any additional physical principle, the power-corrections tend to depend strongly on the details of the…
We consider novel unusual effects in superconductor-ferromagnet (S/F) structures. In particular we analyze the triplet component (TC) of the condensate generated in those systems.This component is odd in frequency and even in the momentum,…