Related papers: The measuring principle and the continuum hypothes…
I prove preservation theorems for countable support iteration of proper forcing concerning certain classes of capacities and submeasures. New examples of forcing notions and connections with measure theory are included.
We study the randomness properties of reals with respect to arbitrary probability measures on Cantor space. We show that every non-computable real is non-trivially random with respect to some measure. The probability measures constructed in…
We generalize the theorems in {\it Mirror Principle I} and {\it II} to the case of general projective manifolds without the convexity assumption. We also apply the results to balloon manifolds, and generalize to higher genus.
We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…
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 attempt to dissolve the measurement problem using an anthropic principle which allows us to invoke rational observers. We argue that the key feature of such observers is that they are rational (we need not care whether they are…
The only evidence we have for a discrete reality comes from quantum measurements; without invoking these measurements, quantum theory describes continuous entities. This seeming contradiction can be resolved via analysis that treats…
The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…
The theory of uniform approximation of real numbers motivates the study of products of consecutive partial quotients in regular continued fractions. For any non-decreasing positive function $\varphi:\mathbb{N}\to [2,\infty)$, we determine…
We strengthen the Free Will Theorem, which proved the spontaneity of particles, based on the free will of the experimenter. The new result is unconditional, and does not require the experimenter's free will to prove the particles'…
One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
In response to a recent rebuttal of [1] presented in [2], we defend the claim that the Consistent Histories formulation of quantum mechanics does not solve the measurement problem. In order to do so, we argue that satisfactory solutions to…
We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of…
There has not been an established mathematical measure of evidence. Some Bayesians have argued that probability can be an objectively correct measure of ``rational degrees of belief,'' which we do not distinguish from evidence. However,…
Adrian Kent has recently presented a critique [arXiv:2307.06191] of our paper [Nat. Comms. 10, 1361 (2019)] in which he claims to refute our main result: the measurement postulates of quantum mechanics can be derived from the rest of…
This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield…
Quantum theory combines density matrices, Born probabilities, tensor-product composites, positive-operator-valued measures (POVMs), and quantum channels. In a finite-dimensional causal operational theory, we prove that two postulates…
Measurement theory is the cornerstone of science, but no equivalent theory underpins the huge volumes of non-numerical data now being generated. In this study, we show that replacing numbers with alternative mathematical models, such as…
We give a self-contained proof of the preservation theorem for proper countable support iterations known as "tools-preservation," "Case A" or "first preservation theorem" in the literature. We do not assume that the forcings add reals.