Related papers: Nested-set inconsistency
This article explores the model-dependent nature of set cardinality, emphasizing that cardinality is not absolute but varies across different axiomatic frameworks. Although Cantor's diagonal argument shows the real numbers are…
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found,…
In this paper we put forward a new solution of the well-known problem of relevant logics, i.e. we construct an atomic entailment. Hence, we construct a system of predicate calculus based on the atomic entailment. Next, we establish the…
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.
The main purpose of this paper is to find the fixed point in such cases where existing literature remain silent. In this paper we introduce partial completeness, a new type of contraction and many other definitions. Using this approach the…
We explore the properties of non-piecewise syndetic sets with positive upper density, which we call "discordant", in countably infinite amenable (semi)groups. Sets of this kind are involved in many questions of Ramsey theory and manifest…
The purpose of this article is to show that on an open and dense set, complete integrability implies the existence of symmetry.
The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…
This paper gives a counterexample to the impossibility, by G\"odel's second incompleteness theorem, of proving a formula expressing the consistency of arithmetic in a fragment of arithmetic on the assumption that the latter is consistent.…
This paper describes problems concerning the range of cardinalities of sumsets and restricted sumsets of finite subsets of the integers and finite subsets of ordered abelian groups.
Intuitive Set Theory (IST) is defined as the theory we get, when we add Axiom of Monotonicity and Axiom of Fusion to Zermelo-Fraenkel set theory. In IST, Continuum Hypothesis is a theorem, Axiom of Choice is a theorem, Skolem paradox does…
This paper is the concise addition to the foregoing work "Inconsistency of Inaccessibility", containing the presentation of main theorem proof (in ZF) about inaccessible cardinals nonexistence. Here some refinement of this presentation is…
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).
The cumulative hierarchy conception of set, which is based on the conception that sets are inductively generated from "former" sets, is generally considered a good way to create a set conception that seems safe from contradictions. This…
We prove, for stably computably enumerable formal systems, direct analogues of the first and second incompleteness theorems of G\"odel. A typical stably computably enumerable set is the set of Diophantine equations with no integer…
The consistency formula for set theory can be stated in terms of the free-variables theory of primitive recursive maps. Free-variable p. r. predicates are decidable by set theory, main result here, built on recursive evaluation of p. r. map…
The new axiom in set theory, axiom of the empty sets, allows another way to formulate Bell inequality in quantum mechanics. The new axiom emerges from the historical and philosophical analysis of set theory.
We present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite…
This paper proves the existence of a dichotomy which being formally derived from the topological successiveness of w-order leads to the same absurdity of Zeno's Dichotomy II. It also derives a contradictory result from the first Zeno's…