Related papers: A beginner's guide to forcing
The purpose of this paper is to develop and study recursive proofs of coinductive predicates. Such recursive proofs allow one to discover proof goals in the construction of a proof of a coinductive predicate, while still allowing the use of…
Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…
It was realized early on that topologies can model constructive systems, as the open sets form a Heyting algebra. After the development of forcing, in the form of Boolean-valued models, it became clear that, just as over ZF any…
We present three natural combinatorial properties for class forcing notions, which imply the forcing theorem to hold. We then show that all known sufficent conditions for the forcing theorem (except for the forcing theorem itself),…
The objective of the present work -- a literature review on both gapped and gapless fractonic theories -- is to pedagogically fill in the gaps between the research on fractons, and an undergraduate physics education (particularly quantum…
In these lectures we hope to provide an elementary introduction to selected topics in light-front dynamics. Starting from the study of free field theories of scalar boson, fermion, and massless vector boson, the canonical field commutators…
In this paper, we study (zero) forcing sets which induce connected subgraphs of a graph. The minimum cardinality of such a set is called the connected forcing number of the graph. We provide sharp upper and lower bounds on the connected…
In this paper, we deal with the notions of naturality from category theory and definablity from model theory and their interactions. In this regard, we present three results. First, we show, under some mild conditions, that naturality…
In the Zermelo--Fraenkel set theory with the Axiom of Choice a forcing notion is "$\kappa$-distributive" if and only if it is "$\kappa$-sequential". We show that without the Axiom of Choice this equivalence fails, even if we include a weak…
The notion of forcing sets for perfect matchings was introduced by Harary, Klein, and \v{Z}ivkovi\'{c}. The application of this problem in chemistry, as well as its interesting theoretical aspects, made this subject very active. In this…
We introduce the concept of inverse powerset by adding three axioms to the Zermelo-Fraenkel set theory. This extends the Zermelo-Fraenkel set theory with a new type of set which is motivated by an intuitive meaning and interesting…
Newtonian gravity can be regarded as a hypothetic-deductive system where the inverse square law is the starting point from which gravitational phenomena are deduced. This operational form of presenting gravity endorses problem solving and…
In this paper, we present a proof of the consistency of the New Foundations set theory ($\mathit{NF}$). $\mathit{NF}$'s main idea is to permit very large sets (including the Universal Set) by restricting set formation to stratified…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
This paper revisits the Pearson Chi-squared independence test. After presenting the underlying theory with modern notations and showing new way of deriving the proof, we describe an innovative and intuitive graphical presentation of this…
We prove a variety of theorems about stationary set reflection and concepts related to internal approachability. We prove that an implication of Fuchino-Usuba relating stationary reflection to a version of Strong Chang's Conjecture cannot…
We introduce the idea of a coherent adequate set of models, which can be used as side conditions in forcing. As an application we define a forcing poset which adds a square sequence on $\omega_2$ using finite conditions.
A connected forcing set of a graph is a zero forcing set that induces a connected subgraph. In this paper, we introduce and study CF-dense graphs -- graphs in which every vertex belongs to some minimum connected forcing set. We identify…
I wrote this book in a "do-it-yourself" style so that I give only a draft of tensor theory, which includes formulating definitions and theorems and giving basic ideas and formulas. All other work such as proving consistence of definitions,…